Daily Papers

From a viewpoint of stochastic thermodynamics, we derive equations that describe the collective dynamics near the order-disorder transition in the globally coupled XY model and near the synchronization-desynchronization transition in the Kuramoto model. A new way of thinking is to interpret the deterministic time evolution of a macroscopic variable as an external operation to a thermodynamic system. We then find that the irreversible work determines the equation for the collective dynamics. When analyzing the Kuramoto model, we employ a generalized concept of irreversible work which originates from a non-equilibrium identity associated with steady state thermodynamics.

The paper has two goals: It presents basic ideas, notions, and methods for reduction of reaction kinetics models: quasi-steady-state, quasi-equilibrium, slow invariant manifolds, and limiting steps. It describes briefly the current state of the art and some latest achievements in the broad area of model reduction in chemical and biochemical kinetics, including new results in methods of invariant manifolds, computation singular perturbation, bottleneck methods, asymptotology, tropical equilibration, and reaction mechanism skeletonisation.

A new type of cooperativity termed temporal cooperativity [Biophys. Chem. 105 585-593 (2003), Annu. Rev. Phys. Chem. 58 113-142 (2007)], emerges in the signal transduction module of phosphorylation-dephosphorylation cycle (PdPC). It utilizes multiple kinetic cycles in time, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein. In the present paper, we thoroughly investigate both the deterministic (microscopic) and stochastic (mesoscopic) models, and focus on the identification of the source of temporal cooperativity via comparing with allosteric cooperativity. A thermodynamic analysis confirms again the claim that the chemical equilibrium state exists if and only if the phosphorylation potential triangle G=0, in which case the amplification of sensitivity is completely abolished. Then we provide comprehensive theoretical and numerical analysis with the first-order and zero-order assumptions in phosphorylation-dephosphorylation cycle respectively. Furthermore, it is interestingly found that the underlying mathematics of temporal cooperativity and allosteric cooperativity are equivalent, and both of them can be expressed by "dissociation constants", which also characterizes the essential differences between the simple and ultrasensitive PdPC switches. Nevertheless, the degree of allosteric cooperativity is restricted by the total number of sites in a single enzyme molecule which can not be freely regulated, while temporal cooperativity is only restricted by the total number of molecules of the target protein which can be regulated in a wide range and gives rise to the ultrasensitivity phenomenon.

The paper sets forth comprehensive basics of Discrete Thermodynamics of Chemical Equilibria (DTD), developed by the author during the last decade and spread over series of publications. Based on the linear equations of irreversible thermodynamics, De Donder's definition of the thermodynamic force, and the Le Chatelier principle, DTD brings forward a notion of chemical equilibrium as a balance of internal and external thermodynamic forces, acting against a chemical system. The basic expression of DTD is a logistic map that ties together energetic characteristics of the chemical transformation in the system, its deviation from true thermodynamic equilibrium, and the sum of thermodynamic forces, causing that deviation. System deviation from thermodynamic equilibrium is the major variable of the theory. Solutions to the basic map define the chemical system domain of states comprising bifurcation diagrams with four areas, from true thermodynamic equilibrium to chaos, having specific distinctive meaning for chemical systems. The theory is derived from the currently recognized ideas of chemical thermodynamics and binds classical and contemporary thermodynamics of chemical equilibria into a unique concept. DTD opens new opportunities in understanding and analysis of equilibria in chemical systems. Some new results, included in the paper, have never been published before.

We provide a concise framework for generalized ensemble theory through a matrix-based approach. By introducing an observation matrix, any discrete probability distribution, including those for non-equilibrium steady states, can be expressed as a generalized Boltzmann distribution, with observables and conjugate variables as the basis and coordinates in a linear space. In this framework, we identify the minimal sufficient statistics required for inferring the Boltzmann distribution. Furthermore, we show that the Hadamard and Vandermonde matrices are suitable observation matrices for spin systems and random walks. In master equation systems, the probability flux observation matrix facilitates the identification of detailed balance violations. Our findings provide a new approach to developing generalized ensemble theory for non-equilibrium steady-state systems.

Macroscopic entropy production σ^{(tot)} in the general nonlinear isothermal chemical reaction system with mass action kinetics is decomposed into a free energy dissipation and a house-keeping heat: σ^{(tot)}=σ^{(fd)}+σ^{(hk)}; σ^{(fd)}=-rd A/rd t, where A is a generalized free energy function. This yields a novel nonequilibrium free energy balance equation rd A/rd t=-σ^{(tot)}+σ^{(hk)}, which is on a par with celebrated entropy balance equation rd S/rd t=σ^{(tot)}+η^{(ex)} where η^{(ex)} is the rate of entropy exchange with the environment.For kinetic systems with complex balance, σ^{(fd)} and σ^{(hk)} are the macroscopic limits of stochastic free energy dissipation and house-keeping heat, which are both nonnegative, in the Delbrück-Gillespie description of the stochastic chemical kinetics.Therefore, we show that a full kinetic and thermodynamic theory of chemical reaction systems that transcends mesoscopic and macroscopic levels emerges.

Understanding the training dynamics of deep neural networks remains a major open problem, with physics-inspired approaches offering promising insights. Building on this perspective, we develop a thermodynamic framework to describe the stationary distributions of stochastic gradient descent (SGD) with weight decay for scale-invariant neural networks, a setting that both reflects practical architectures with normalization layers and permits theoretical analysis. We establish analogies between training hyperparameters (e.g., learning rate, weight decay) and thermodynamic variables such as temperature, pressure, and volume. Starting with a simplified isotropic noise model, we uncover a close correspondence between SGD dynamics and ideal gas behavior, validated through theory and simulation. Extending to training of neural networks, we show that key predictions of the framework, including the behavior of stationary entropy, align closely with experimental observations. This framework provides a principled foundation for interpreting training dynamics and may guide future work on hyperparameter tuning and the design of learning rate schedulers.

The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added subsequently to that original work, to explore the consequences of the purely statistical point of view. We show how standard methods in the equilibrium theory could have been derived simply from a description of the available problem information. In addition, our presentation leads to novel insights into questions associated with symmetry and non-equilibrium statistical mechanics. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a quantity related to the thermodynamic entropy production is found by considering information loss in non-equilibrium processes. Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complexity by successively adding information to create progressively more complex descriptions of a physical system. Our result is that such statistical mechanical descriptions can be used to create transparent, computable, experimentally-relevant models that may be informed by more detailed atomistic simulations. We also derive a theory for the kinetic behavior of this system, identifying the nonequilibrium `process' free energy functional. The Gibbs relation for this functional is a fluctuation-dissipation theorem applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient driving forces. Based on this work, it is clear that statistical mechanics is a general tool for constructing the relationships between constraints on system information.

We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative log-likelihood of the data that relates model performance to entropy rates of diffusion processes. We numerically validate this bound on a synthetic dataset and investigate its tightness. By building a bridge to entropy rates - system, intrinsic, and exchange entropy - we provide new insights into the thermodynamic operation of these models, drawing parallels to Maxwell's demon and implications for thermodynamic computing hardware. Our framework connects generative modeling performance to fundamental physical principles through stochastic thermodynamics.

In this paper I apply newly-proposed information-theoretic principles to thermodynamic work extraction. I show that if it is possible to extract work deterministically from a physical system prepared in any one of a set of states, then those states must be distinguishable from one another. This result is formulated independently of scale and of particular dynamical laws; it also provides a novel connection between thermodynamics and information theory, established via the law of conservation of energy (rather than the second law of thermodynamics). Albeit compatible with these conclusions, existing thermodynamics approaches cannot provide a result of such generality, because they are scale-dependent (relying on ensembles or coarse-graining) or tied to particular dynamical laws. This paper thus provides a broader foundation for thermodynamics, with implications for the theory of von Neumann's universal constructor

We show how to extract from a sufficiently long time series of stationary fluctuations of chemical reactions an estimate of the entropy production. This method, which is based on recent work on fluctuation theorems, is direct, non-invasive, does not require any knowledge about the underlying dynamics, and is applicable even when only partial information is available. We apply it to simple stochastic models of chemical reactions involving a finite number of states, and for this case, we study how the estimate of dissipation is affected by the degree of coarse-graining present in the input data.

Large language models (LLMs) are increasingly considered as tutoring aids in science education. Yet their readiness for unsupervised use in undergraduate instruction remains uncertain, as reliable teaching requires more than fluent recall: it demands consistent, principle-grounded reasoning. Thermodynamics, with its compact laws and subtle distinctions between state and path functions, reversibility, and entropy, provides an ideal testbed for evaluating such capabilities. Here we present UTQA, a 50-item undergraduate thermodynamics question answering benchmark, covering ideal-gas processes, reversibility, and diagram interpretation. No leading 2025-era model exceeded our 95\% competence threshold: the best LLMs achieved 82\% accuracy, with text-only items performing better than image reasoning tasks, which often fell to chance levels. Prompt phrasing and syntactic complexity showed modest to little correlation with performance. The gap concentrates in finite-rate/irreversible scenarios and in binding visual features to thermodynamic meaning, indicating that current LLMs are not yet suitable for unsupervised tutoring in this domain.

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. These systems generically involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the magnitude of the steady-state probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry and the strength of nonequilibrium transport of measure. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework that estimates the score of this density. We show that the score, together with the microscopic equations of motion, gives direct access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles, spatial regions, and degrees of freedom. To represent the score, we introduce a novel, spatially-local transformer-based network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of interacting active particles undergoing motility-induced phase separation (MIPS). We show that a single instance of our network trained on a system of 4096 particles at one packing fraction can generalize to other regions of the phase diagram, including systems with as many as 32768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.

Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create inhomogeneities that can dramatically affect the reaction rate. The extreme case is that of a reaction coupled to a phase transformation, whose kinetics must depend on the order parameter -- and its gradients, at phase boundaries. This Account presents a general theory of chemical kinetics based on nonequilibrium thermodynamics. The reaction rate is a nonlinear function of the thermodynamic driving force (free energy of reaction) expressed in terms of variational chemical potentials. The Cahn-Hilliard and Allen-Cahn equations are unified and extended via a master equation for non-equilibrium chemical thermodynamics. For electrochemistry, both Marcus and Butler-Volmer kinetics are generalized for concentrated solutions and ionic solids. The theory is applied to intercalation dynamics in the phase separating Li-ion battery material Li_xFePO_4.

We investigate the time evolution of the Boltzmann entropy of a dilute gas of N particles, N>>1, as it undergoes a free expansion doubling its volume. The microstate of the system, a point in the 4N dimensional phase space, changes in time via Hamiltonian dynamics. Its entropy, at any time t, is given by the logarithm of the phase space volume of all the microstates giving rise to its macrostate at time t. The macrostates that we consider are defined by coarse graining the one-particle phase space into cells Δ_α. The initial and final macrostates of the system are equilibrium states in volumes V and 2V, with the same energy E and particle number N. Their entropy per particle is given, for sufficiently large systems, by the thermodynamic entropy as a function of the particle and energy density, whose leading term is independent of the size of the Δ_α. The intermediate (non-equilibrium) entropy does however depend on the size of the cells Δ_α. Its change with time is due to (i) dispersal in physical space from free motion and to (ii) the collisions between particles which change their velocities. The former depends strongly on the size of the velocity coarse graining Δv: it produces entropy at a rate proportional to Δv. This dependence is investigated numerically and analytically for a dilute two-dimensional gas of hard discs. It becomes significant when the mean free path between collisions is of the same order or larger than the length scale of the initial spatial inhomogeneity. In the opposite limit, the rate of entropy production is essentially independent of Δv and is given by the Boltzmann equation for the limit Δvrightarrow 0. We show that when both processes are active the time dependence of the entropy has a scaling form involving the ratio of the rates of its production by the two processes.

All current formulations of thermodynamics invoke some form of coarse-graining or ensembles as the supposed link between their own laws and the microscopic laws of motion. They deal only with ensemble-averages, expectation values, macroscopic limits, infinite heat baths, etc., not with the details of physical variables of individual microscopic systems. They are consistent with the laws of motion for finite systems only in certain approximations, which improve with increasing scale, given various assumptions about initial conditions which are neither specified precisely nor even thought to hold exactly in nature. Here I propose a new formulation of the zeroth, first and second laws, improving upon the axiomatic approach to thermodynamics (Carath\'eodory, 1909; Lieb & Yngvason, 1999), via the principles of the recently proposed constructor theory. Specifically, I provide a non-approximative, scale-independent formulation of 'adiabatic accessibility'; this in turn provides a non-approximative, scale-independent distinction between work and heat and reveals an unexpected connection between information theory and the first law of thermodynamics (not just the second). It also achieves the long-sought unification of the axiomatic approach with Kelvin's.

All known up to now models of chemical oscillations are based exclusively on kinetic considerations. The chemical gross-process equation is split usually by elementary steps, each step is supplied by an arrow and a differential equation, joint solution to such a construction under certain, often ad hoc chosen conditions and with ad hoc numerical coefficients leads to chemical oscillations. Kinetic perception of chemical oscillations reigns without exclusions. However, as it was recently shown by the author for the laser and for the electrochemical systems, chemical oscillations follow also from solutions to the basic expressions of discrete thermodynamics of chemical equilibria. Graphically those solutions are various fork bifurcation diagrams, and, in certain types of chemical systems, oscillations are well pronounced in the bistable bifurcation areas. In this work we describe a general thermodynamic approach to chemical oscillations as opposite to kinetic models, and depict some of their new features like spontaneity and fractality. The paper doubts exclusivity of the kinetic approach to chemical oscillations, and its aim is to discuss and exemplify thermodynamically predicted chemical oscillations in closed chemical systems.

Boltzmann generators approach the sampling problem in many-body physics by combining a normalizing flow and a statistical reweighting method to generate samples in thermodynamic equilibrium. The equilibrium distribution is usually defined by an energy function and a thermodynamic state. Here we propose temperature-steerable flows (TSF) which are able to generate a family of probability densities parametrized by a choosable temperature parameter. TSFs can be embedded in generalized ensemble sampling frameworks to sample a physical system across multiple thermodynamic states.

The transition from the superconducting to the normal state in a magnetic field was considered as a irreversible thermodynamic process before 1933 because of Joule heating. But all physicists became to consider this transition as reversible after 1933 because of the obvious contradiction of the Meissner effect with the second law of thermodynamics if this transition is considered as a irreversible process. This radical change of the opinion contradicted logic since the dissipation of the kinetic energy of the surface screening current into Joule heat in the normal state cannot depend on how this current appeared in the superconducting state. The inconsistency of the conventional theory of superconductivity, created in the framework of the equilibrium thermodynamics, with Joule heating, on which Jorge Hirsch draws reader's attention, is a consequence of this history. In order to avoid contradiction with the second law of thermodynamics, physicists postulated in the thirties of the last century that the surface screening current is damped without the generation of Joule heat. This postulate contradicts not only logic and the conventional theory of superconductivity but also experimental results.

We formulate nonequilibrium thermodynamics in which intensive variables acquire operational meaning through measurement protocols consistent with local reciprocity. Using physical equilibrium as a reference, conjugate observables are constructed by continuously adjusting devices along the local tangent space of the statistical manifold. In this relativity of observation, Onsager reciprocity holds locally, allowing inference-based Lagrange multipliers to be directly measured. This provides a systematic method to extend operational definitions of intensive variables to nonequilibrium states, highlighting their context-dependent nature and offering a concrete experimental strategy.

The principle of detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process. For many real physico-chemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions etc), detailed mechanisms include both reversible and irreversible reactions. In this case, the principle of detailed balance cannot be applied directly. We represent irreversible reactions as limits of reversible steps and obtain the principle of detailed balance for complex mechanisms with some irreversible elementary processes. We proved two consequences of the detailed balance for these mechanisms: the structural condition and the algebraic condition that form together the extended form of detailed balance. The algebraic condition is the principle of detailed balance for the reversible part. The structural condition is: the convex hull of the stoichiometric vectors of the irreversible reactions has empty intersection with the linear span of the stoichiometric vectors of the reversible reaction. Physically, this means that the irreversible reactions cannot be included in oriented pathways. The systems with the extended form of detailed balance are also the limits of the reversible systems with detailed balance when some of the equilibrium concentrations (or activities) tend to zero. Surprisingly, the structure of the limit reaction mechanism crucially depends on the relative speeds of this tendency to zero.

We apply the Nakajima-Zwanzig approach to open quantum systems to study steady-state transport across generic multi-level junctions coupled to bosonic or fermionic reservoirs. The method allows for a unified diagrammatic formulation in Liouville space, with diagrams being classified according to an expansion in the coupling strength between the reservoirs and the junction. Analytical, approximate expressions are provided up to fourth order for the steady-state boson transport that generalize to multi-level systems the known results for the low-temperature thermal conductance in the spin-boson model. The formalism is applied to the problem of heat transport in a qubit-resonator junction modeled by the quantum Rabi model. Nontrivial transport features emerge as a result of the interplay between the qubit-oscillator detuning and coupling strength. For quasi-degenerate spectra, nonvanishing steady-state coherences cause a suppression of the thermal conductance.

Can a micron sized sack of interacting molecules understand, and adapt to a constantly-fluctuating environment? Cellular life provides an existence proof in the affirmative, but the principles that allow for life's existence are far from being proven. One challenge in engineering and understanding biochemical computation is the intrinsic noise due to chemical fluctuations. In this paper, we draw insights from machine learning theory, chemical reaction network theory, and statistical physics to show that the broad and biologically relevant class of detailed balanced chemical reaction networks is capable of representing and conditioning complex distributions. These results illustrate how a biochemical computer can use intrinsic chemical noise to perform complex computations. Furthermore, we use our explicit physical model to derive thermodynamic costs of inference.

We theoretically identify the noise-induced coherent contribution to the ergotropy of a four-level quantum heat engine coupled to a unimodal quantum cavity. We utilize a protocol where the passive state's quasiprobabilities can be analytically identified from the population-coherence coupled reduced density matrix. The reduced density matrix elements are evaluated using a microscopic quantum master equation formalism. Multiple ergotropies within the same coherence interval, each characterized by a positive and pronounced coherent contribution, are observed. These ergotropies are a result of population inversion as well as quasiprobability-population inversion, controllable through the coherence measure parameters. The optimal flux and power of the engine are found to be at moderate values of ergotropy with increasing values of noise-induced coherence. The optimal power at different coherences is found to possess a constant ergotropy.

Building upon a thermodynamic formalism, we show that self-gravitating systems in hydrostatic equilibrium with a uniform density are maximal entropy states when submitted to perturbations which are slow on dynamical timescale. We coin this phenomenon "thermodynamic blocking", given its similarity with the more general "kinetic blocking". This result underlines the importance of the thermodynamic formalism which proves useful when kinetic equations break down.

We study an autonomous model of a Maxwell demon that works by rectifying thermal fluctuations of chemical reactions. It constitutes the chemical analog of a recently studied electronic demon. We characterize its scaling behavior in the macroscopic limit, its performances, and the impact of potential internal delays. We obtain analytical expressions for all quantities of interest, namely, the generated reverse chemical current, the output power, the transduction efficiency, and the correlations between the numbers of molecules. Due to a bound on the nonequilibrium response of its chemical reaction network, we find that, contrary to the electronic case, there is no way for the Maxwell demon to generate a finite output in the macroscopic limit. Finally, we analyze the information thermodynamics of the Maxwell demon from a bipartite perspective. In the limit of a fast demon, the information flow is obtained, its pattern in the state space is discussed, and the behavior of the partial efficiencies related to the measurement and the feedback processes is examined.

This paper introduces Galactic Bioware's Life Support System, a semi-closed-circuit breathing apparatus designed for integration into a positive-pressure firefighting suit and governed by an AI control system. The breathing loop incorporates a soda lime CO2 scrubber, a silica gel dehumidifier, and pure O2 replenishment with finite consumables. One-way exhaust valves maintain positive pressure while creating a semi-closed system in which outward venting gradually depletes the gas inventory. Part I develops the physicochemical foundations from first principles, including state-consistent thermochemistry, stoichiometric capacity limits, adsorption isotherms, and oxygen-management constraints arising from both fire safety and toxicity. Part II introduces an AI control architecture that fuses three sensor tiers, external environmental sensing, internal suit atmosphere sensing (with triple-redundant O2 cells and median voting), and firefighter biometrics. The controller combines receding-horizon model-predictive control (MPC) with a learned metabolic model and a reinforcement learning (RL) policy advisor, with all candidate actuator commands passing through a final control-barrier-function safety filter before reaching the hardware. This architecture is intended to optimize performance under unknown mission duration and exertion profiles. In this paper we introduce an 18-state, 3-control nonlinear state-space formulation using only sensors viable in structural firefighting, with triple-redundant O2 sensing and median voting. Finally, we introduce an MPC framework with a dynamic resource scarcity multiplier, an RL policy advisor for warm-starting, and a final control-barrier-function safety filter through which all actuator commands must pass, demonstrating 18-34% endurance improvement in simulation over PID baselines while maintaining tighter physiological and fire-safety margins.

This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary approaches emerging in research groups around the world.

This paper develops a comprehensive theoretical framework that imports concepts from stochastic thermodynamics to model price impact and characterize the feasibility of round-trip arbitrage in financial markets. A trading cycle is treated as a non-equilibrium thermodynamic process, where price impact represents dissipative work and market noise plays the role of thermal fluctuations. The paper proves a Financial Second Law: under general convex impact functionals, any round-trip trading strategy yields non-positive expected profit. This structural constraint is complemented by a fluctuation theorem that bounds the probability of profitable cycles in terms of dissipated work and market volatility. The framework introduces a statistical ensemble of trading strategies governed by a Gibbs measure, leading to a free energy decomposition that connects expected cost, strategy entropy, and a market temperature parameter. The framework provides rigorous, testable inequalities linking microstructural impact to macroscopic no-arbitrage conditions, offering a novel physics-inspired perspective on market efficiency. The paper derives explicit analytical results for prototypical trading strategies and discusses empirical validation protocols.

We study the problem of the transformation of a given reactant species into an immiscible product species, as they flow through a chemically active porous medium. We derive the equation governing the evolution of the volume fraction of the species -- in a one-dimensional macroscopic description --, identify the relevant dimensionless numbers, and provide simple models for capillary pressure and relative permeabilities, which are quantities of crucial importance when tackling multiphase flows in porous media. We set the domain of validity of our models and discuss the importance of viscous coupling terms in the extended Darcy's law. We investigate numerically the steady regime and demonstrate that the spatial transformation rate of the species along the reactor is non-monotonous, as testified by the existence of an inflection point in the volume fraction profiles. We obtain the scaling of the location of this inflection point with the dimensionless lengths of the problem. Eventually, we provide key elements for optimization of the reactor.

Second-order training methods have better convergence properties than gradient descent but are rarely used in practice for large-scale training due to their computational overhead. This can be viewed as a hardware limitation (imposed by digital computers). Here we show that natural gradient descent (NGD), a second-order method, can have a similar computational complexity per iteration to a first-order method, when employing appropriate hardware. We present a new hybrid digital-analog algorithm for training neural networks that is equivalent to NGD in a certain parameter regime but avoids prohibitively costly linear system solves. Our algorithm exploits the thermodynamic properties of an analog system at equilibrium, and hence requires an analog thermodynamic computer. The training occurs in a hybrid digital-analog loop, where the gradient and Fisher information matrix (or any other positive semi-definite curvature matrix) are calculated at given time intervals while the analog dynamics take place. We numerically demonstrate the superiority of this approach over state-of-the-art digital first- and second-order training methods on classification tasks and language model fine-tuning tasks.

We show that PLDR-LLMs pretrained at self-organized criticality exhibit reasoning at inference time. The characteristics of PLDR-LLM deductive outputs at criticality is similar to second-order phase transitions. At criticality, the correlation length diverges, and the deductive outputs attain a metastable steady state. The steady state behaviour suggests that deductive outputs learn representations equivalent to scaling functions, universality classes and renormalization groups from the training dataset, leading to generalization and reasoning capabilities in the process. We can then define an order parameter from the global statistics of the model's deductive output parameters at inference. The reasoning capabilities of a PLDR-LLM is better when its order parameter is close to zero at criticality. This observation is supported by the benchmark scores of the models trained at near-criticality and sub-criticality. Our results provide a self-contained explanation on how reasoning manifests in large language models, and the ability to reason can be quantified solely from global model parameter values of the deductive outputs at steady state, without any need for evaluation of curated benchmark datasets through inductive output for reasoning and comprehension.

Approximations based on moment-closure (MA) are commonly used to obtain estimates of the mean molecule numbers and of the variance of fluctuations in the number of molecules of chemical systems. The advantage of this approach is that it can be far less computationally expensive than exact stochastic simulations of the chemical master equation. Here we numerically study the conditions under which the MA equations yield results reflecting the true stochastic dynamics of the system. We show that for bistable and oscillatory chemical systems with deterministic initial conditions, the solution of the MA equations can be interpreted as a valid approximation to the true moments of the CME, only when the steady-state mean molecule numbers obtained from the chemical master equation fall within a certain finite range. The same validity criterion for monostable systems implies that the steady-state mean molecule numbers obtained from the chemical master equation must be above a certain threshold. For mean molecule numbers outside of this range of validity, the MA equations lead to either qualitatively wrong oscillatory dynamics or to unphysical predictions such as negative variances in the molecule numbers or multiple steady-state moments of the stationary distribution as the initial conditions are varied. Our results clarify the range of validity of the MA approach and show that pitfalls in the interpretation of the results can only be overcome through the systematic comparison of the solutions of the MA equations of a certain order with those of higher orders.

We construct the charged Hayward-anti-de Sitter (AdS) black hole (BH) with a cloud of strings (CS) and perfect fluid dark matter (PFDM), and analyze its extended thermodynamic phase structure. The Hayward parameter g replaces the central singularity with a de Sitter (dS) core, while the CS parameter a and the PFDM parameter β encode astrophysically motivated matter content. Treating the cosmological constant as pressure, we derive the thermodynamic quantities, verify the Smarr relation, and establish P--V criticality with a van der Waals (vdW)-like small-large BH phase transition and mean-field critical exponents. The Gibbs free energy (GFE) exhibits the characteristic swallowtail below the critical pressure. The Joule-Thomson (JT) expansion yields T_i^{rm min}/T_c approx 0.247, roughly half the Reissner--Nordström-AdS value. The parameters g and Q contract the cooling region, β expands it, and a reshapes it non-monotonically. A holographic heat engine with a rectangular cycle gives efficiencies η= 0.362--0.396 and Carnot benchmarking ratios η/η_C = 0.625--0.791 across six configurations. The CS parameter improves the engine efficiency by reducing the enthalpy at fixed thermodynamic volume, while the PFDM parameter degrades it by adding gravitational enthalpy without contributing to the mechanical work.

In this work, we embark on the thermodynamic investigation concerning a family of primary charged black holes within the context of shift and parity symmetric Beyond Horndeski gravity. Employing the Euclidean approach, we derive the functional expression for the free energy and derive the first thermodynamic law, offering a methodology to address the challenge of extracting the thermal quantities in shift-symmetric scalar tensor theories characterized by linear time dependence in the scalar field. Following the formal analysis, we provide some illustrative examples focusing on the thermal evaporation of these fascinating objects.

We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect of random advection and diffusion and encompassing as specific cases, some models studied in the literature, like the Kang-Redner, Kipnis-Marchioro-Presutti, Takayasu-Taguchi, etc. The motivation for our setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. For finite lattices, we study both the coalescence of an initially spread field (interpreted as roughening), and the statistical steady-state properties. We distinguish two main size-dependent regimes, depending on the strength of the diffusion term and on the lattice size. Using numerical simulations and mean-field approach, we study the statistics of the field. For weak diffusion, we unveil a characteristic hierarchical structure of the field. We also connect the model and the iterated function systems concept.

In this work, we introduce a novel approach for predicting thermodynamic properties of binary mixtures, which we call the similarity-based method (SBM). The method is based on quantifying the pairwise similarity of components, which we achieve by comparing quantum-chemical descriptors of the components, namely σ-profiles. The basic idea behind the approach is that mixtures with similar pairs of components will have similar thermodynamic properties. The SBM is trained on a matrix that contains some data for a given property for different binary mixtures; the missing entries are then predicted by the SBM. As an example, we consider the prediction of isothermal activity coefficients at infinite dilution (γ^infty_{ij}) and show that the SBM outperforms the well-established physical methods modified UNIFAC (Dortmund) and COSMO-SAC-dsp. In this case, the matrix is only sparsely occupied, and it is shown that the SBM works also if only a limited number of data for similar mixtures is available. The SBM idea can be transferred to any mixture property and is a powerful tool for generating essential data for many applications.

The Mean Spherical Approximation (MSA) is a commonly-used thermodynamic theory for computing the energetics of ions in the primitive model (i.e., charged hard-sphere ions in a background dielectric). For the excess chemical potential, however, the early MSA formulations (which were widely adopted) only included the terms needed to compute the mean excess chemical potential (or the mean activity coefficient). Other terms for the chemical potential μ_i of individual species i were not included because they sum to 0 in the mean chemical potential. Here, we derive these terms to give a complete MSA formulation of the chemical potential. The result is a simple additive term for μ_i that we show is a qualitative improvement over the previous MSA version. In addition, our derivation shows that the MSA's assumption of global charge neutrality is not strictly necessary, so that the MSA is also valid for systems close to neutrality.

An obstacle to artificial general intelligence is set by continual learning of multiple tasks of different nature. Recently, various heuristic tricks, both from machine learning and from neuroscience angles, were proposed, but they lack a unified theory ground. Here, we focus on continual learning in single-layered and multi-layered neural networks of binary weights. A variational Bayesian learning setting is thus proposed, where the neural networks are trained in a field-space, rather than gradient-ill-defined discrete-weight space, and furthermore, weight uncertainty is naturally incorporated, and modulates synaptic resources among tasks. From a physics perspective, we translate the variational continual learning into Franz-Parisi thermodynamic potential framework, where previous task knowledge acts as a prior and a reference as well. We thus interpret the continual learning of the binary perceptron in a teacher-student setting as a Franz-Parisi potential computation. The learning performance can then be analytically studied with mean-field order parameters, whose predictions coincide with numerical experiments using stochastic gradient descent methods. Based on the variational principle and Gaussian field approximation of internal preactivations in hidden layers, we also derive the learning algorithm considering weight uncertainty, which solves the continual learning with binary weights using multi-layered neural networks, and performs better than the currently available metaplasticity algorithm. Our proposed principled frameworks also connect to elastic weight consolidation, weight-uncertainty modulated learning, and neuroscience inspired metaplasticity, providing a theory-grounded method for the real-world multi-task learning with deep networks.

We prove existence of weak and strong solutions and uniqueness for a viscous dyadic model driven by additive white noise in time using a path-wise approach. Existence of invariant measures also established and a simple balance relation among the mean rates of energy injection, dissipation and flux is derived and we investigate the asymptotic exponents zeta_{p} of the p-order structure functions.

In this paper, we develop and implement an efficient asymptotic-preserving (AP) scheme to solve the gas mixture of Boltzmann equations under the disparate mass scaling relevant to the so-called "epochal relaxation" phenomenon. The disparity in molecular masses, ranging across several orders of magnitude, leads to significant challenges in both the evaluation of collision operators and the designing of time-stepping schemes to capture the multi-scale nature of the dynamics. A direct implementation of the spectral method faces prohibitive computational costs as the mass ratio increases due to the need to resolve vastly different thermal velocities. Unlike [I. M. Gamba, S. Jin, and L. Liu, Commun. Math. Sci., 17 (2019), pp. 1257-1289], we propose an alternative approach based on proper truncation of asymptotic expansions of the collision operators, which significantly reduces the computational complexity and works well for small varepsilon. By incorporating the separation of three time scales in the model's relaxation process [P. Degond and B. Lucquin-Desreux, Math. Models Methods Appl. Sci., 6 (1996), pp. 405-436], we design an AP scheme that captures the specific dynamics of the disparate mass model while maintaining computational efficiency. Numerical experiments demonstrate the effectiveness of the proposed scheme in handling large mass ratios of heavy and light species, as well as capturing the epochal relaxation phenomenon.

Heat pumps are essential for decarbonizing residential heating but consume substantial electrical energy, impacting operational costs and grid demand. Many systems run inefficiently due to planning flaws, operational faults, or misconfigurations. While optimizing performance requires skilled professionals, labor shortages hinder large-scale interventions. However, digital tools and improved data availability create new service opportunities for energy efficiency, predictive maintenance, and demand-side management. To support research and practical solutions, we present an open-source dataset of electricity consumption from 1,408 households with heat pumps and smart electricity meters in the canton of Zurich, Switzerland, recorded at 15-minute and daily resolutions between 2018-11-03 and 2024-03-21. The dataset includes household metadata, weather data from 8 stations, and ground truth data from 410 field visit protocols collected by energy consultants during system optimizations. Additionally, the dataset includes a Python-based data loader to facilitate seamless data processing and exploration.

In the language domain, as in other domains, neural explainability takes an ever more important role, with feature attribution methods on the forefront. Many such methods require considerable computational resources and expert knowledge about implementation details and parameter choices. To facilitate research, we present Thermostat which consists of a large collection of model explanations and accompanying analysis tools. Thermostat allows easy access to over 200k explanations for the decisions of prominent state-of-the-art models spanning across different NLP tasks, generated with multiple explainers. The dataset took over 10k GPU hours (> one year) to compile; compute time that the community now saves. The accompanying software tools allow to analyse explanations instance-wise but also accumulatively on corpus level. Users can investigate and compare models, datasets and explainers without the need to orchestrate implementation details. Thermostat is fully open source, democratizes explainability research in the language domain, circumvents redundant computations and increases comparability and replicability.

Uncovering the rules governing the nonequilibrium dynamics of the membranes that define biological cells is of central importance to understanding the physics of living systems. We theoretically and computationally investigate the behavior of flexible quasispherical vesicles that exchange membrane constituents, internal volume, and heat with an external reservoir. The excess chemical potential and osmotic pressure difference imposed by the reservoir act as generalized thermodynamic driving forces that modulate vesicle morphology. We show that the renormalization of membrane mechanical properties by nonequilibrium driving gives rise to a morphological transition between a weakly driven regime, in which growing vesicles remain quasispherical, and a strongly driven regime, in which vesicles accommodate rapid membrane uptake by developing surface wrinkles. Additionally, we propose a minimal vesicle growth-shape law, derived using insights from stochastic thermodynamics, that robustly describes vesicle growth dynamics even in strongly driven, far-from-equilibrium regimes.

Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which can be challenging for large, strongly-correlated systems. This issue has motivated the study of physically-inspired dynamical approaches such as thermodynamic cooling. In this work, we introduce a ground-state preparation algorithm based on the simulation of quantum dynamics. Our main insight is to transform the Hamiltonian by a shifted sign function via quantum signal processing, effectively mapping eigenvalues into positive and negative subspaces separated by a large gap. This automatically ensures that all states within each subspace conserve energy with respect to the transformed Hamiltonian. Subsequent time-evolution with a perturbed Hamiltonian induces transitions to lower-energy states while preventing unwanted jumps to higher energy states. The approach does not rely on a priori knowledge of energy gaps and requires no additional qubits to model a bath. Furthermore, it makes mathcal{O}(d^{,3/2}/epsilon) queries to the time-evolution operator of the system and mathcal{O}(d^{,3/2}) queries to a block-encoding of the perturbation, for d cooling steps and an epsilon-accurate energy resolution. Our results provide a framework for combining quantum signal processing and Hamiltonian simulation to design heuristic quantum algorithms for ground-state preparation.

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology, geophysics, astrophysics and fluid dynamics. In the PINN framework, the governing partial differential equations, along with initial and boundary conditions, are encoded directly into the loss function, enabling the network to learn solutions that are consistent with the underlying physics. In this work, we employ the PINN framework to solve the dimensionless Navier-Stokes equations for three two-dimensional incompressible, steady, laminar flow problems without using any labeled data. The boundary and initial conditions are enforced in a hard manner, ensuring they are satisfied exactly rather than penalized during training. We validate the PINN predicted velocity profiles, drag coefficients and pressure profiles against the conventional computational fluid dynamics (CFD) simulations for moderate to high values of Reynolds number (Re). It is observed that the PINN predictions show good agreement with the CFD results at lower Re. We also extend our analysis to a transient condition and find that our method is equally capable of simulating complex time-dependent flow dynamics. To quantitatively assess the accuracy, we compute the L_2 normalized error, which lies in the range O(10^{-4}) - O(10^{-1}) for our chosen case studies.