arXiv research

Introduces q-paths for generalizing geometric annealing paths in machine learning.

Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous success in describing, among others, the particular stationary state correspondin…

Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter $q$. A generalized form of the Black-Scholes (B-S) partial differential equation, and some closed-form solutions are obtained. The standard B-S equation ($q=1…

The cornerstone of Boltzmann-Gibbs ($BG$) statistical mechanics is the Boltzmann-Gibbs-Jaynes-Shannon entropy $S_{BG} \equiv -k\int dx f(x)\ln f(x)$, where $k$ is a positive constant and $f(x)$ a probability density function. This theory has exibited, along more than one century, great success in the treatment of syste…

Stock market indices are one of the most investigated complex systems in econophysics. Here we extend the existing literature on stock markets in connection with nonextensive statistical mechanics. We explore the nonextensivity of price volatilities for 34 major stock market indices between 2010 and 2019. We discover t…

Study detects anomalies in financial markets using GNN and nonextensive entropy.

Estimate relaxation times in nonextensive systems using gradient flow for Tsallis entropy maximization.

We seek to utilize the nonextensive statistics to the microscopic modeling of the interacting many-investor dynamics that drive the price changes in a market. The statistics of price changes are known to be fit well by the Students-T and power-law distributions of the nonextensive statistics. We therefore derive models…

We analyze the cumulative distribution of total personal income of USA counties, and gross domestic product of Brazilian, German and United Kingdom counties, and also of world countries. We verify that generalized exponential distributions, related to nonextensive statistical mechanics, describe almost the whole spectr…

Engle's ARCH algorithm is a generator of stochastic time series for financial returns (and similar quantities) characterized by a time-dependent variance. It involves a memory parameter $b$ ($b=0$ corresponds to {\it no memory}), and the noise is currently chosen to be Gaussian. We assume here a generalized noise, name…

In this paper we present an interacting-agent model of stock markets. We describe a stock market through an Ising-like model in order to formulate the tendency of traders getting to be influenced by the other traders' investment attitudes [1], and formulate the traders' decision-making regarding investment as the maxim…

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 sensitivity to risk that most people (hence, financial operators) feel affects the dynamics of financial transactions. Here we present an approach to this problem based on a current generalization of Boltzmann-Gibbs statistical mechanics.

The thermodynamics of markets is analyzed, revealing parallels with thermodynamic laws.

New framework reveals thermodynamic principles for LLM training.

This study compares different thermodynamic structure-informed neural networks for solving differential equations.

Geometric approach to quantum thermodynamics models state spaces and processes.

Constructions of metrics with special holonomy by methods of exterior differential systems are reviewed and the interpretations of these construction as `flows' on hypersurface geometries are considered. It is shown that these hypersurface 'flows' are not generally well-posed for smooth initial data and counterexamples…

We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy $S_{q}=k\frac{1-\sum\limits_{i=1}^{W} p_{i} ^{q}}{1-q} (q\in \Re)$ ($S_{1} \equiv S_{BG}=-k\sum\limits_{i=1}^{W}p_{i} \l…

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…

Study on thermodynamic costs of simple linear regression.

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 statistics of return distributions on various time scales constitutes one of the most informative characteristics of the financial dynamics. Here we present a systematic study of such characteristics for the Polish stock market index WIG20 over the period 04.01.1999 - 31.10.2005 for the time lags ranging from one m…

Geometric study of thermodynamics using cotangent bundles.

Financial market dynamics compared to thermodynamics.

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.

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.

Upper bound derived for informed traders' gains in a model, akin to 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.

The paper provides a geometric framework for understanding non-equilibrium thermodynamics.

Work maximization guides machine learning models in adaptive systems.

Develops thermodynamic formalism for quasimorphisms on negatively curved spaces.

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.

Develops neural networks for learning physics of complex systems by enforcing thermodynamics principles.

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.

TANNs integrate thermodynamics into ANN models for accurate, consistent predictions.

A thermodynamic theory explains EU election vote distributions.

Proof of boundedness of quasimorphisms for certain Lie groups.

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…