# Entropy production in systems with unidirectional transitions

## TL;DR

This paper develops a framework for defining and analyzing entropy production in systems with a mixture of unidirectional and bidirectional transitions, extending thermodynamic concepts to more complex stochastic systems.

## Contribution

It introduces a method to define average entropy production in systems with unidirectional links, preserving fluxes and providing physical interpretation.

## Key findings

- The framework is consistent with thermodynamics.
- Systems with unidirectional cycles behave pseudo-deterministically.
- Application to stochastic resetting reveals links between time arrow and entropy production.

## Abstract

The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each transition between two states also the reverse one is allowed. Nevertheless, several physical systems may exhibit a mixture of both unidirectional and bidirectional transitions, and how to properly define the entropy production in this case is still an open question. Here, we present a solution to such a challenging problem. The average entropy production can be consistently defined, employing a mapping that preserves the average fluxes, and its physical interpretation is provided. We describe a class of stochastic systems composed of unidirectional links forming cycles and detailed-balanced bidirectional links, showing that they behave in a pseudo-deterministic fashion. This approach is applied to a system with time-dependent stochastic resetting. Our framework is consistent with thermodynamics and leads to some intriguing observations on the relation between the arrow of time and the average entropy production for resetting events.