This study compares different thermodynamic structure-informed neural networks for solving differential equations.
problem Improving the accuracy and physical consistency of neural network solutions to differential equations.
method Comprehensive evaluation of various thermodynamic formulations in physics-informed neural networks.
result Newtonian-residual-based PINNs fail to reliably recover physical quantities, while structure-preserving formulations enhance accuracy and robustness.
Financial market dynamics compared to thermodynamics.
problem Understanding the dynamics of financial markets through thermodynamic principles.
method Analogy with Szilárd information engine to derive market temperature and information extraction.
result Informed traders' gains are bounded by market temperature and information.
By treating the financial market as a thermodynamic system, we establish a one-to-one correspondence between thermodynamic variables and economic quantities. Measured by the expected loss under the worst-case scenario, financial risk caused by model uncertainty is regarded as a result of the interaction between financi…
Upper bound derived for informed traders' gains in a model, akin to thermodynamics.
problem Informed traders' gains in a financial model with finite horizon.
method Bayesian inference and entropic inequality.
result Upper bound for expected gain, analogous to thermodynamics.
How do organisms recognize their environment by acquiring knowledge about the world, and what actions do they take based on this knowledge? This article examines hypotheses about organisms' adaptation to the environment from machine learning, information-theoretic, and thermodynamic perspectives. We start with construc…
Geometric approach to thermodynamics of chemical reaction networks.
problem Thermodynamics of chemical reaction networks with non-ideal behavior.
method Information geometry, Riemannian geometry, Cramer-Rao bound, absolute sensitivity.
result Absolute sensitivity is a projection operator onto the tangent bundle of the equilibrium manifold.
The paper uses thermodynamics to improve machine learning representation quality.
problem Improving the quality of learned representations for transfer learning.
method Formal connection with thermodynamics, iso-classification process, traversing the equilibrium surface.
result Demonstrates how to transfer representations while keeping classification loss constant.
This work develops a machine learning approach to EOS models that accounts for thermodynamic constraints and model uncertainty.
problem Developing accurate equation of state models for high energy-density experiments with inherent uncertainties.
method Physics-informed Gaussian process regression (GPR) framework to capture model uncertainty and thermodynamic constraints.
result The proposed framework reduces prediction uncertainty by incorporating thermodynamic constraints, as demonstrated for diamond carbon EOS.
Develops neural networks for learning physics of complex systems by enforcing thermodynamics principles.
problem Learning physics of complex systems from incomplete experimental data.
method Integrates port-metriplectic formalism with neural networks to enforce thermodynamics principles.
result Neural networks can learn physics of complex systems by parts, reducing learning burden.
The article explores how organisms and machines learn and recognize the world using Bayesian inference and thermodynamics.
problem Understanding how organisms and machines learn and recognize the world.
method Introducing a thermodynamic view of the Bayesian brain hypothesis, using a simple generative model of spiking neural populations.
result The process of Bayesian inference can be quantified using entropy, revealing the perceptual capacity of neural activity.
Introduce a thermodynamically informed, temperature-transferable MLCG framework for proteins.
problem Temperature transferability of MLCG models for proteins.
method Explicit decomposition of CG potential into energetic and entropic components.
result Reproduces temperature-dependent quantities like heat capacity.
Urban transformations within large and growing metropolitan areas often generate critical dynamics affecting social interactions, transport connectivity and income flow distribution. We develop a statistical-mechanical model of urban transformations, exemplified for Greater Sydney, and derive a thermodynamic descriptio…
Unified thermodynamic approach to Transformer attention dynamics.
problem Understanding the statistical mechanics of Transformer attention.
method Constructing a Lagrangian on the information manifold to analyze attention dynamics.
result Establishes a formal correspondence between scaled dot-product attention and canonical ensemble statistics.
The formal structure of geometrical thermodynamics is reviewed with particular emphasis on the geometry of equilibria submanifolds. On these submanifolds thermodynamic metrics are defined as the Hessian of thermodynamic potentials. Links between geometry and thermodynamics are explored for single and multiple component…
The thermodynamics of markets is analyzed, revealing parallels with thermodynamic laws.
problem Understanding economic systems through thermodynamic principles.
method Derivation and analysis of thermodynamic laws applied to economic systems.
result Deep analogy between thermodynamic and economic parameters established.
Paper uses referenced thermodynamic integration for Bayesian model selection in a complex COVID-19 transmission model.
problem Bayesian model selection with uncertainty and misleading metrics.
method Referenced thermodynamic integration for intractable high-dimensional distributions.
result Favourable convergence performance in model selection for COVID-19 transmission.
New framework reveals thermodynamic principles for LLM training.
problem Understanding the training dynamics of large language models.
method Introducing Neural Thermodynamic Laws (NTL) under river-valley loss landscape assumptions.
result Key thermodynamic quantities and principles naturally emerge in LLM training.
The paper clarifies thermodynamics on non-compact symmetric spaces using Kähler geometry.
problem Formulating thermodynamics on non-compact symmetric spaces U/H. method Introducing a distinction between thermodynamics of dynamical systems and Gibbs distributions, proving only Kähler spaces support Gibbs distributions, solving the temperature space problem.
result Only Kähler spaces support Gibbs distributions on non-compact symmetric spaces U/H. Geometric approach to quantum thermodynamics models state spaces and processes.
problem Quantum thermodynamics in the regime of non-equilibrium states.
method Contact geometry and principal fiber bundles to model quantum state spaces and processes.
result Geometric formulation reveals the fundamental thermodynamic relations and unattainability of the third law.
Extends likelihood ratio exponential families to analyze various optimization methods.
problem Analyzing optimization methods like rate-distortion and information bottleneck.
method Linking geometric mixture paths to exponential families and using hypothesis testing.
result Provides a common mathematical framework for understanding these methods.
A family of replicator-like dynamics, called the escort replicator equation, is constructed using information-geometric concepts and generalized information entropies and diverenges from statistical thermodynamics. Lyapunov functions and escort generalizations of basic concepts and constructions in evolutionary game th…
Physics-informed machine learning models improve biomolecular system simulations.
problem Modeling unresolved interactions beyond classical force fields.
method Physics-informed neural networks and operator learning.
result Accurate, mechanistic, generalizable models for long-timescale kinetics.
Two new metrics assess LLM faithfulness and entropy, improving model reliability.
problem Evaluating the accuracy of LLMs in generating coherent responses.
method Proposes SF and SEP metrics based on information theory and thermodynamics.
result High SF and SEP scores indicate more faithful LLM responses.
A new method uses heat diffusion to efficiently solve combinatorial optimization problems.
problem Challenges in combinatorial optimization due to discrete nature and limited search scope.
method Transforming the target function through heat diffusion to enable information flow and more efficient navigation.
result Superior performance across various combinatorial optimization problems.
Study on thermodynamic costs of simple linear regression.
problem Understanding thermodynamic costs in machine learning models.
method Approximated thermodynamic lower bounds for exact and stochastic linear regression.
result Derived scaling laws for optimal dataset size based on generalization error.
Geometric structures help in understanding thermodynamics.
problem Understanding thermodynamic systems using geometric methods.
method Using almost cosymplectic structures and variational arguments.
result Evolution equations are derived and discussed.
Diffusion models' speed-accuracy relations derived from thermodynamics.
problem Understanding the trade-off between model speed and accuracy.
method Connecting diffusion models to thermodynamics and optimal transport.
result Speed-accuracy relations derived, providing insights into optimal learning protocols.
PA reinterpreted as SB problem, unifying thermodynamics and optimal transport.
problem Optimizing discrete-time paths between probability distributions.
method Schrödinger Bridge theory, solving variational problems.
result PA's reweighting step derived from Schrödinger system.
Deep neural networks learn by averaging fast variables, revealing a Gaussian process.
problem Analyzing the complex behavior of deep neural networks (DNNs) with billions of parameters.
method Identifying slow variables that average the erratic behavior of fast microscopic variables in fully trained DNNs.
result DNN layers couple only through the second moment (kernels) of their activations and pre-activations, which fluctuate in a nearly Gaussian manner.
Geometric study of thermodynamics using cotangent bundles.
problem Formulating classical thermodynamics using geometric structures.
method Contact geometry on cotangent bundles, homogeneous coordinates for intensive variables.
result Geometric formulation of thermodynamics with homogeneity properties.
The article reviews how gradient flow systems on hypergraphs connect to information geometry and nonequilibrium physics.
problem Understanding the geometry of perturbed gradient flow systems on hypergraphs.
method Formulating modern nonequilibrium principles within the framework of perturbed gradient flow systems on hypergraphs.
result New concepts like moduli spaces and thermodynamical area are introduced to understand speed limits.
For common people, in contrast to brokers, bankers, and those who play on rising and falling prices of stocks, the stock market law is based on the simple fact that the depositors aim for financial profit at any given concrete stage. The common depositor cannot cause any significant variations in prices. This concept s…
The author proposes a finance trading strategy named Entropy Oriented Trading and apply thermodynamics on the strategy. The state variables are chosen so that the strategy satisfies the second law of thermodynamics. Using the law, the author proves that the rate of investment (ROI) of the strategy is equal to or more t…
The paper applies thermodynamics to financial markets to prove no-arbitrage constraints.
problem No arbitrage in financial markets under price impact.
method Stochastic thermodynamics applied to financial trading cycles.
result Proves any round-trip trading strategy yields non-positive expected profit.
New Holder bounds improve variational inference by flattening thermodynamic curves.
problem Improving variational inference by addressing performance gaps between theory and practice.
method Generalizing thermodynamic integration to weighted Holder mean, introducing Holder bounds.
result Holder bounds promise a one-step approximation of exact marginal log-likelihood.
We propose a new method of valuation of portfolios and their respective investing strategies. To this end we define a canonical ensemble of portfolios that allows to use the formalism thermodynamics.
Schrödinger and Onsager's ideas linked in nonequilibrium thermodynamics.
problem Linking Schrödinger's variational problem with Onsager's nonequilibrium statistical mechanics.
method Analyzing the historical context and comparing the two approaches.
result Schrödinger's ideas have not yet been fully integrated into the classical context of Onsager's work.
In this work we offer a framework for reasoning about a wide class of existing objectives in machine learning. We develop a formal correspondence between this work and thermodynamics and discuss its implications.
The paper provides a geometric framework for understanding non-equilibrium thermodynamics.
problem Unclear geometric structure of GENERIC in non-equilibrium thermodynamics.
method Cotangent lifts of dynamics, splitting into holonomic and vertical representatives, and formulation within contact geometry.
result Physical meaning and explicit formulation of the second law of thermodynamics within evolution equations.
Work maximization guides machine learning models in adaptive systems.
problem How machine learning models can be optimized for thermodynamic efficiency.
method Introducing thermodynamic principle to compare with maximum-likelihood principle.
result Maximum-work models are equivalent to maximum-likelihood models in adaptive systems.
Develops thermodynamic formalism for quasimorphisms on negatively curved spaces.
problem Analyzing quasimorphisms on negatively curved spaces.
method Thermodynamic formalism framework, Banach isomorphism, weak Livšic cohomology.
result Establishes Central Limit Theorem and invariance principle for unbounded quasimorphisms.
Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equa- tions for nonequilibrium thermodynamics admit an intrinsic formulation in …
We study the indefinite metric G in the contact phase space (P,θ) of a homogeneous thermodynamical system introduced by R. Mrugala. We calculate the curvature tensor, Killing vector fields, second fundamental form of Legendre submanifolds of P - constitutive surfaces of different homogeneous thermodynamical syste…
We formulate thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic variables and their determination is reduced to the computation of the partition…
We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase space is odd-dimensional. For a system with n thermodynamic degrees of freedom it …
Rate GENERIC extends thermodynamics principles to non-equilibrium systems.
problem Understanding non-equilibrium thermodynamics and its relation to equilibrium thermodynamics.
method Developed a geometrical framework for rate GENERIC, extending Onsager's variational principle.
result Rate GENERIC structure provides a new perspective on thermodynamics in non-equilibrium systems.
TANNs integrate thermodynamics into ANN models for accurate, consistent predictions.
problem Lack of rigorous physics-based approach in ANN constitutive modeling.
method TANNs encode thermodynamics principles in neural network architecture using automatic differentiation.
result TANNs produce thermodynamically consistent predictions without requiring large datasets.
A thermodynamic theory explains EU election vote distributions.
problem Describing EU election vote distributions.
method Tracing parallels between system energies of coupled nonlinear oscillators and party vote fractions.
result The Rayleigh-Jeans (RJ) theory well depicts EU vote results and candidate vote dispersion.