Entropy production in continuous systems with unidirectional transitions

TL;DR

This paper derives a formula for entropy production in continuous stochastic systems with unidirectional transitions, revealing that entropy flux is related to the divergence of the rate vector and vanishes in Hamiltonian systems.

Contribution

It introduces a continuous-space expression for entropy production in systems with unidirectional transitions, extending previous discrete models.

Findings

Entropy flux equals the negative divergence of the rate vector.

In Hamiltonian systems, entropy flux is zero.

Derived from the continuous limit of discrete stochastic dynamics.

Abstract

We derive the expression for the entropy production for stochastic dynamics defined on a continuous space of states containing unidirectional transitions. The expression is derived by taking the continuous limit of a stochastic dynamics on a discrete space of states and is based on an expression for the entropy production appropriate for unidirectional transition. Our results shows that the entropy flux is the negative of the divergence of the vector firld whose components are the rates at which a dynamic variable changes in time. For a Hamiltonian dynamical system, it follows from this result that the entropy flux vanish identically.