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.
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.
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.
Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a …
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.
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…
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.
Develops neural networks that follow thermodynamics principles.
problem Learning physical systems from data while respecting thermodynamics.
method Uses feedforward neural networks and the GENERIC formalism to enforce metriplectic structure.
result Predictions comply with first and second principles of thermodynamics.
Framework preserves emergent physics in non-equilibrium systems from particle trajectories.
problem Linking short spatiotemporal scales to emergent bulk physics in multiscale systems.
method Metriplectic bracket formalism for structure-preserving coarse-graining.
result Preservation of thermodynamic laws and conservation in machine-learned dynamics.
Unified framework for training diffusion and flow models to sample from target distributions.
problem Training diffusion and flow models to sample from target distributions defined by exponential tilting.
method Unified framework combining stochastic optimal control and non-equilibrium thermodynamics perspectives.
result Unified bias-variance decompositions and theoretical support for adjoint-based methods.
Generative diffusion models exhibit phase transitions in statistical mechanics, impacting their performance.
problem Understanding the performance and capabilities of generative diffusion models.
method Reformulating generative diffusion models using statistical mechanics, focusing on phase transitions and symmetry breaking.
result Generative diffusion models undergo second-order phase transitions with mean-field universality, critical instability, and mean-field critical exponents.
This article derives prognostic expressions for the evolution of globally aggregated economic wealth, productivity, inflation, technological change, innovation and growth. The approach is to treat civilization as an open, non-equilibrium thermodynamic system that dissipates energy and diffuses matter in order to sustai…
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and…
New CGMD model predicts non-equilibrium processes better than existing methods.
problem Inconsistency in conditional distribution of unresolved variables.
method Time-lagged independent component analysis to minimize entropy contribution of unresolved variables.
result The model's generalization ability for non-equilibrium processes is significantly improved.
Alternative finance models from physics for non-equilibrium systems.
problem Inequities of classical finance models in physics-based perspective.
method Physics-based insights for non-equilibrium finance models.
result Alternative models for non-equilibrium finance systems.
A new method relaxes molecules without needing non-equilibrium data.
problem Molecular relaxation requires understanding non-equilibrium structures.
method MoreRed: molecular relaxation by reverse diffusion with time step prediction.
result MoreRed learns a simpler pseudo potential energy surface.
Neural network models colloidal particle dynamics in non-equilibrium systems.
problem Analyzing non-equilibrium dynamics of many-body colloidal systems.
method Combining power functional theory and machine learning, training a neural network to predict internal force fields.
result The neural network accurately predicts dynamics in non-equilibrium systems, in good agreement with simulations.
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 paper studies geometric properties of hydrodynamical density manifolds.
problem Understanding the geometry of hydrodynamical density manifolds.
method Formulating connections, gradients, Hessians, parallel transports, and curvatures on these manifolds.
result Closed-form formulas for sectional curvatures in one-dimensional density manifolds.
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.
Mathematical model predicts international trade and global economy dynamics.
problem Understanding complex international trade and economy interactions.
method Developed a mathematical model for non-equilibrium processes in open systems.
result Predicted model accurately reflects international trade and economy.
Investigates spontaneous symmetry breaking in non-equilibrium systems.
problem Spontaneous symmetry breaking of ergodicity in non-equilibrium systems.
method Mathematical and effective field theory approaches to investigate symmetry breaking.
result Symmetry breaking phenomena observed in stochastic processes.
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.
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.
A new method uses deep learning to predict rare events in complex systems.
problem Predicting rare and extreme events in non-equilibrium systems.
method A deep learning approach that minimizes the geometrical action.
result The method accurately predicts rare events in various complex systems.
Paper connects RL and non-equilibrium statistical mechanics for entropy-regularized RL.
problem Obtaining analytical solutions for entropy-regularized RL.
method Mapping RL to non-equilibrium statistical mechanics, applying large deviation theory.
result Derives exact analytical results for optimal policy and dynamics in MDPs.
We analyze the statistics of daily price change of stock market in the framework of a statistical physics model for the collective fluctuation of stock portfolio. In this model the time series of price changes are coded into the sequences of up and down spins, and the Hamiltonian of the system is expressed by spin-spin…
In this paper I give a brief introduction to a family of simple but non-trivial models designed to increase our understanding of collective processes in markets, the so-called Minority Games, and their non-equilibrium statistical mathematical analysis. Since the most commonly studied members of this family define disor…
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.
Investigates fluid flow perturbations using geometric theory.
problem Analyzing linear perturbations in non-equilibrium fluid flows.
method Uses second order variations of the action and Jacobi fields.
result Demonstrates numerical simulations of perturbation dynamics.
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.
New method reconstructs non-equilibrium stochastic systems from data.
problem Reconstructing non-equilibrium stochastic systems from ensemble measurements.
method Schrödinger bridge problem with multivariate Ornstein-Uhlenbeck process.
result Simulation-free algorithm achieves higher accuracy than competing methods.
Develops a method for non-equilibrium importance sampling to estimate expectations and constants.
problem Estimating expectations and normalization constants for complex high-dimensional distributions.
method Generates samples from a base distribution, transports them using a velocity field, and averages along flowlines.
result The method can achieve zero-variance estimation and significantly reduces variance compared to vanilla estimators.
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.
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.
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 origin of the long-range memory in the non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases a notion of spurious memory is introduced. A good example of Markov processes with spurious memory is stochastic process driven by a non-…
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.
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.
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.
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.
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.
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 …
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.