Non-equilibrium entropy and irreversibility in generalized stochastic Loewner evolution from an information-theoretic perspective

TL;DR

This paper explores the non-equilibrium entropy and irreversibility in generalized stochastic Loewner evolution using information theory, deriving new thermodynamic relations and verifying non-equilibrium behavior through numerical simulations.

Contribution

It introduces an information-theoretic framework for encoding non-equilibrium processes in SLE, deriving entropy production, flux, and reformulating thermodynamic equalities.

Findings

Derived entropy production and flux for 2D SLE trajectories.

Reformulated thermodynamic relations using Kullback-Leibler divergence.

Numerically verified non-equilibrium properties via long-time simulations.

Abstract

The generalized stochastic Loewner evolution (SLE) driven by reversible Langevin dynamics was theoretically investigated in the context of non-equilibrium statistical mechanics. The recent study of the authors revealed that the Loewner evolution enables encoding the non-equilibrium (irreversible) processes into equilibrium (reversible) processes. In this study, by Gibbs entropy-based information-theoretic approaches, we formulated this encoding mechanism of the SLE to discuss its advantages as a mean to better describe non-equilibrium states. After deriving entropy production and flux for the 2D trajectories of the generalized SLE curve, we reformulated the system's entropic properties in terms of the Kullback-Leibler (KL) divergence. We demonstrate that this operation leads to alternative expressions of the Jarzynski equality and the second law of thermodynamics, which are consistent with the previously suggested theory of information thermodynamics. The irreversibility of the 2D trajectory was likewise discussed by decomposing its entropy into additive and non-additive parts. We numerically verified the non-equilibrium property of our model by simulating the long-time behavior of the entropic measure suggested by our formulation, referred to as the relative Loewner entropy.