Entropy production along a deterministic motion

TL;DR

This paper introduces a stochastic framework linked to deterministic differential equations to analyze entropy production and flux, revealing that entropy flux equals the negative divergence of the velocity field, with no flux in Hamiltonian systems.

Contribution

It presents a novel stochastic dynamics associated with deterministic motion and derives explicit formulas for entropy production and flux in this context.

Findings

Entropy flux equals negative divergence of velocity field

Entropy production is derived from the stochastic dynamics

Hamiltonian dynamics have zero entropy flux

Abstract

We propose a stochastic dynamics to be associated to a deterministic motion defined by a set of first order differential equation. The transitions that defined the stochastic dynamics are unidirectional and the rates are equal to the absolute value of the velocity vector field associate to the deterministic motion. From the stochastic dynamics we determine the entropy production and the entropy flux. This last quantity is found to be the negative of the divergence of the velocity vector field. In the case of a Hamiltonian dynamics it vanishes identically.