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…
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48 results for “Thermodynamics”
Thermodynamics of marketsq-fin.GN
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.
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.
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.
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 Thermodynamic Costs of Simple Linear Regressioncond-mat.stat-mech
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.
Speed-accuracy relations for diffusion models: Wisdom from nonequilibrium thermodynamics and optimal transportcond-mat.stat-mech
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.
Population Annealing as a Discrete-Time Schrödinger Bridgecond-mat.stat-mech
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.
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 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.
The thermodynamics of portfolioscond-mat.stat-mech
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.
Stochastic Geometric Mechanics in Nonequilibrium Thermodynamics: Schrödinger meets Onsagercond-mat.stat-mech
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.
On the role of geometry in statistical mechanics and thermodynamics I: Geometric perspectivecond-mat.stat-mech
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.
Thermodynamic Machine Learning through Maximum Work Productioncond-mat.stat-mech
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 …
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.
We study the indefinite metric in the contact phase space of a homogeneous thermodynamical system introduced by R. Mrugala. We calculate the curvature tensor, Killing vector fields, second fundamental form of Legendre submanifolds of - 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 …
On the role of geometry in statistical mechanics and thermodynamics II: Thermodynamic perspectivecond-mat.stat-mech
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.
Thermodynamic theory of voting and EU electionscond-mat.stat-mech
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.
Proof of boundedness of quasimorphisms for certain Lie groups.
problem Bounding quasimorphisms on lattices in Lie groups.
method Thermodynamic formalism applied to bounded cohomology.
result Every π-quasimorphism on irreducible uniform lattices is bounded.
The present paper analyses the formal parallelism existing between the laws of thermodynamics and some economic principles. Based on previous works, we shall show how the existence in Economics of principles analogous to those in thermodynamics involves the occurrence of economic events that remind of well-known phenom…
Learning Stochastic Thermodynamics Directly from Correlation and Trajectory-Fluctuation Currentscond-mat.stat-mech
New method learns stochastic thermodynamics from system currents.
problem Understanding entropy production in complex dynamical systems.
method Constructs learning framework using currents and machine learning loss functions.
result Derives loss functions for thermodynamic functions directly from dynamics.
Unified framework for understanding TVO and improving model learning.
problem Improving the tightness and efficiency of variational inference bounds.
method Exponential family interpretation and equal spacing in moment parameters.
result Unified framework and improved gradient estimator for TVO.
We introduce thermodynamic response functions for singular Bayesian models.
problem Singular Bayesian models violate regular asymptotics due to non-identifiability and degenerate Fisher geometry.
method Posterior tempering induces thermodynamic response functions, linking WAIC, WBIC, and singular fluctuation.
result WAIC, WBIC, and singular fluctuation are unified within a thermodynamic response framework.
The paper clarifies thermodynamics on non-compact symmetric spaces using Kähler geometry.
problem Formulating thermodynamics on non-compact symmetric spaces .
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 .
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…
Geometrically describes pseudo-gauge freedom in relativistic hydrodynamics.
problem Pseudo-gauge ambiguity in relativistic hydrodynamics.
method Develops -contact geometry to describe thermodynamic states and conservation laws.
result Identifies pseudo-gauge freedom as the non-uniqueness of thermodynamic equilibrium redefinition.
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.
Economic Cycles of Carnot Typeq-fin.GN
Originally, the Carnot cycle is a theoretical thermodynamic cycle that provides an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of…
The principles of adaptation in organisms and machines II: Thermodynamics of the Bayesian brainq-bio.NC
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.
The paper solves a thermodynamics problem about crystal shape.
problem Understanding if minimizing free energy with convex potential and mass constraint generates a convex crystal.
method Utilized a stability theorem, convexity, and a new maximum principle approach to prove a three-dimensional convexity theorem.
result Completely settled the Almgren problem in under generic conditions.
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…
The Thermodynamic Approach to Whole-Life Insurance: A Method for Evaluation of Surrender Riskq-fin.GN
Model evaluates insurance risk using thermodynamic principles.
problem Risk of lapses due to adverse selection in insurance.
method Collective model with diffusion process influenced by statistical mechanics.
result Derives level premium to evaluate insurance risk.
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.
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.
We set forth a definition of hyperfinite knots. Loosely speaking, these are limits of certain sequences of knots with increasing crossing number. These limits exist in appropriate closures of quotient spaces of knots. We give examples of hyperfinite knots. These examples stem from an application of the Thermodynamic Li…