A generalized detailed balance relation

TL;DR

This paper derives a generalized detailed balance relation for systems interacting with an active bath containing metastable solute molecules, accounting for multiple reaction channels and heat exchange.

Contribution

It introduces a generalized detailed balance relation that incorporates multiple reaction channels and heat exchange with an active bath.

Findings

The ratio of transition probabilities is a weighted sum over channels.

Each channel's ratio depends on the heat released during the reaction.

The relation accounts for complex interactions with an active, reactive environment.

Abstract

Given a system $M$ in a thermal bath we obtain a generalized detailed balance relation for the ratio $r=\pi_\tau(K\to J)/\pi_\tau(J\to K)$ of the transition probabilities $M:J\to K$ and $M:K\to J$ in time $\tau$. We assume an active bath, containing solute molecules in metastable states. These molecules may react with $M$ and the transition $J\to K$ occurs through different channels $\alpha$ involving different reactions with the bath. We find that $r=\sum p^\alpha r^\alpha$, where $p^\alpha$ is the probability that channel $\alpha$ occurs, and $r^\alpha$ depends on the amount of heat (more precisely enthalpy) released to the bath in channel $\alpha$.