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.
New framework reveals thermodynamic principles for LLM training.
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…
Geometric approach to quantum thermodynamics models state spaces and processes.
The thermodynamics of markets is analyzed, revealing parallels with thermodynamic laws.
Upper bound derived for informed traders' gains in a model, akin to thermodynamics.
Geometrically describes pseudo-gauge freedom in relativistic hydrodynamics.
This study compares different thermodynamic structure-informed neural networks for solving differential equations.
Study on thermodynamic costs of simple linear regression.
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…
In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples. The evolution equations of the involved observables are obtained in each example…
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…
TANNs integrate thermodynamics into ANN models for accurate, consistent predictions.
Researchers create black holes isometric to extremal Reissner-Nordström.
The article explores how organisms and machines learn and recognize the world using Bayesian inference and thermodynamics.
Financial market dynamics compared to thermodynamics.
The paper provides a geometric framework for understanding non-equilibrium thermodynamics.
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 paper applies thermodynamics to financial markets to prove no-arbitrage constraints.
We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the D…
Inspired by constructions in complex geometry we introduce a thermodynamic framework for Monge-Ampère equations on real tori. We show convergence in law of the associated point processes and explain connections to complex Monge-Ampère equations and optimal transport.
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…
Unified thermodynamic approach to Transformer attention dynamics.
This work develops a machine learning approach to EOS models that accounts for thermodynamic constraints and model uncertainty.
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 …
We formulate the variational problem for AdS gravity with Dirichlet boundary conditions and demonstrate that the covariant counterterms are necessary to make the variational problem well-posed. The holographic charges associated with asymptotic symmetries are then rederived via Noether's theorem and `covariant phase sp…
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…
Every production-recycling iteration accumulates an inevitable proportion of its matter-energy in the environment, lest the production process itself would be a system in perpetual motion, violating the second law of Thermodynamics. Such high-entropy matter depletes finite stocks of ecosystem services provided by the e…
Universal model for soft tissue mechanics under shock waves.
Within the description of stochastic differential equations it is argued that the existence of Boltzmann-Gibbs type distribution in economy is independent of the time reversal symmetry in econodynamics. Both power law and exponential distributions can be accommodated by it. The demonstration is based on a mathematical …
Statistical models of economic distributions lead to Boltzmann distributions rather than a Pareto power law. This result is supported by two facts: 1. the distributions of income, car sales, marriages or jobs are a matter of chances and luck and not of reason! 2. Data for property, automobile sales, marriages and job m…
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two characteristic regimes. For large values of wealth it takes the form of a Pareto style…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus can not be used as a standard distribution. Normally professionals in the area …
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 distribution of firms' growth and firms' sizes is a topic under intense scrutiny. In this paper we show that a thermodynamic model based on the Maximum Entropy Principle, with dynamical prior information, can be constructed that adequately describes the dynamics and distribution of firms' growth. Our theoretical fr…
This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various ki…
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…
Geometric structures help in understanding thermodynamics.
Diffusion models' speed-accuracy relations derived from thermodynamics.
PA reinterpreted as SB problem, unifying thermodynamics and optimal transport.
The Sinkhorn flow is a gradient flow in a nonlocal Wasserstein geometry.
Geometric study of thermodynamics using cotangent bundles.
New analysis shows temperature guarantees generalization in stochastic training.
New Holder bounds improve variational inference by flattening thermodynamic curves.
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.
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.
Study characterizes Uniswap v3 liquidity pools using transaction graphs and identifies ideal trading conditions.
Work maximization guides machine learning models in adaptive systems.