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In this work we introduce a method for estimating entropy rate and entropy production rate from finite symbolic time series. From the point of view of statistics, estimating entropy from a finite series can be interpreted as a problem of…

Statistical Mechanics · Physics 2021-02-24 Raul Salgado-Garcia , Cesar Maldonado

Estimating entropy production, which quantifies irreversibility and energy dissipation, remains a significant challenge despite its central role in nonequilibrium physics. We propose a novel method for estimating the mean entropy production…

Statistical Mechanics · Physics 2026-01-05 Ivan Di Terlizzi

We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the Relative Entropy Rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of…

Mathematical Physics · Physics 2013-04-16 Yannis Pantazis , Markos A. Katsoulakis

For a Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE's) time discretization numerical schemes usually destroy the property of…

Numerical Analysis · Mathematics 2019-02-20 Markos Katsoulakis , Yannis Pantazis , Luc Rey-Bellet

This Letter presents a neural estimator for entropy production, or NEEP, that estimates entropy production (EP) from trajectories of relevant variables without detailed information on the system dynamics. For steady state, we rigorously…

Statistical Mechanics · Physics 2020-10-06 Dong-Kyum Kim , Youngkyoung Bae , Sangyun Lee , Hawoong Jeong

Fluctuating entropy production is studied for a set of linearly coupled complex fields. The general result is applied to non-equilibrium fluctuating hydrodynamic equations for coarse-grained fields (density, temperature and velocity), in…

Statistical Mechanics · Physics 2012-07-09 Giacomo Gradenigo , Andrea Puglisi , Alessandro Sarracino

The estimation of entropy rates for stationary discrete-valued stochastic processes is a well studied problem in information theory. However, estimating the entropy rate for stationary continuous-valued stochastic processes has not received…

Information Theory · Computer Science 2021-05-26 Andrew Feutrill , Matthew Roughan

In nature stationary nonequilibrium systems cannot exist on their own, rather they need to be driven from outside in order to keep them away from equilibrium. While the internal mean entropy of such stationary systems is constant, the…

Statistical Mechanics · Physics 2013-10-03 Somayeh Zeraati , Farhad H. Jafarpour , Haye Hinrichsen

Time-reversal symmetry breaking and entropy production are universal features of nonequilibrium phenomena. Despite its importance in the physics of active and living systems, the entropy production of systems with many degrees of freedom…

We study irreversible processes for nonlinear oscillators networks described by complex-valued Langevin equations that account for coupling to different thermo-chemical baths. Dissipation is introduced via non-Hermitian terms in the…

Statistical Mechanics · Physics 2017-08-02 Simone Borlenghi , Stefano Iubini , Stefano Lepri , Jonas Fransson

The information on a quantum process acquired through measurements plays a crucial role in the determination of its non-equilibrium thermodynamic properties. We report on the experimental inference of the stochastic entropy production rate…

This paper shows an estimation of a lower bound on the total entropy production rate(EPR) for a system following Langevin dynamics with a single observed variable coarse-grained into a few discrete states, by invoking the underlying broken…

Statistical Mechanics · Physics 2022-09-07 Aishani Ghosal , Gili Bisker

A rigorous derivation of nonequilibrium entropy production via the path-integral formalism is presented. Entropy production is defined as the entropy change piled in a heat reservoir as a result of a nonequilibrium thermodynamic process. It…

Statistical Mechanics · Physics 2015-10-28 Chulan Kwon

We provide a strategy for an exact inference of the average as well as the fluctuations of the entropy production in non-equilibrium systems in the steady state, from the measurements of arbitrary current fluctuations. Our results are built…

Statistical Mechanics · Physics 2020-03-24 Sreekanth K Manikandan , Deepak Gupta , Supriya Krishnamurthy

Out-of-equilibrium systems continuously generate entropy, with its rate of production being a fingerprint of non-equilibrium conditions. In small-scale dissipative systems subject to thermal noise, fluctuations of entropy production are…

Statistical Mechanics · Physics 2023-01-19 Prajwal Padmanabha , Daniel Maria Busiello , Amos Maritan , Deepak Gupta

A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components. Most of them -- such as global vegetation -- are inherently non-stationary, for example due to strong…

Chaotic Dynamics · Physics 2026-04-28 Taylor Smith , Andreas Morr , Christof Schötz , Niklas Boers

We discuss entropy production in nonequilibrium steady states by focusing on paths obtained by sampling at regular (small) intervals, instead of sampling on each change of the system's state. This allows us to study directly entropy…

Statistical Mechanics · Physics 2011-09-07 Daniel ben-Avraham , Sven Dorosz , Michel Pleimling

Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their…

Machine Learning · Statistics 2021-11-01 Mikhail Genkin , Owen Hughes , Tatiana A. Engel

The entropy production rate (EPR) offers a quantitative measure of time reversal symmetry breaking in non-equilibrium systems. It can be defined either at particle level or at the level of coarse-grained fields such as density; the EPR for…

Statistical Mechanics · Physics 2021-02-03 Yuting I. Li , Michael E. Cates

When analyzing the equilibrium properties of a stochastic process, identifying the parity of the variables under time-reversal is imperative. This initial step is required to assess the presence of detailed balance, and to compute the…

Statistical Mechanics · Physics 2025-04-09 Dario Lucente , Marco Baldovin , Massimiliano Viale , Angelo Vulpiani