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…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “statistical thermodynamics”
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.
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.
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.
I present in this paper some tools in Symplectic and Poisson Geometry in view of their applications in Geometric mechanics and Mathematical Physics. After a short discussion of the Lagrangian and Hamiltonian formalisms, including the use of symmetry groups, and a presentation of the Tulczyjew's isomorphisms (which expl…
Paper optimizes change detection in unnormalized distributions.
problem Detecting changes in unnormalized pre- and post-change distributions.
method Log-Partition Approximation Cumulative Sum (LPA-CUSUM) algorithm based on thermodynamic integration.
result Asymptotically optimal performance achieved through unbiased estimation of CUSUM statistics.
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.
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.
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.
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.
We analyze social and economic systems with a hierarchical structure and show that for such systems, it is possible to construct thermostatistics, based on the intermediate Gentile statistics. We show that in social and economic hierarchical systems there are elements that obey the Fermi-Dirac statistics and can be cal…
We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper arXiv:0811.2801. In particular, the thermodynamic partition function of molten crystals is shown to be equal to the classical limit of the par…
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…
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…
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.
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.
Minimum-Excess-Work Guidancestat.ML
Proposes a thermodynamic work minimization framework for guiding generative models.
problem Guiding generative models in sparse-data regimes with limited target samples or constraints.
method Regularization framework inspired by thermodynamic work, introducing Path Guidance and Observable Guidance.
result Improves sample efficiency and reduces bias in molecular 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…
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.
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.
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.
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.
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…
BMTI method estimates densities without bins, outperforming traditional estimators.
problem Nonparametric, robust, and data-efficient density estimation in high-dimensional spaces.
method BMTI integrates log-density differences between neighboring points, weighted by uncertainties, using a maximum-likelihood formulation.
result BMTI reconstructs smooth profiles in high-dimensional spaces, outperforming traditional estimators.
Active learning of Boltzmann samplers and potential energies with quantum mechanical accuracyphysics.chem-ph
New method combines deep learning and quantum mechanics for efficient molecular statistics.
problem Computational expense in extracting statistics from molecular systems.
method Adaptive Markov chain Monte Carlo with Normalizing Flow and MLP for quantum accuracy.
result Rapid convergence to Boltzmann distribution and accurate thermodynamic observables.
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.
Euclidean and Riemannian Geometrical Approaches to Non-Extensive Thermo-Statistical Mechanicscond-mat.stat-mech
I introduce a new geometrical approach to thermo--statistical mechanics. Here I highlight the main physical ideas, and how do they translate into geometrical language. I contrast the present approach with previous thermo--statistical--geometrical formalisms, (pseudo-)Riemannian [Weinhold 1975; Ruppeiner 1979] as well a…
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.
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.
Eventological H-theoremq-fin.MF
We prove the eventological -theorem that complements the Boltzmann H-theorem from statistical mechanics and serves as a mathematical excuse (mathematically no less convincing than the Boltzmann H-theorem for the second law of thermodynamics) for what can be called "the second law of eventology", which justifies the …
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…
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.
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.
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.
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…