Stochastic thermodynamics of chemical reaction networks

TL;DR

This paper develops a stochastic thermodynamic framework for chemical reaction networks, defining energy, entropy, and fluctuation theorems at the level of individual reaction trajectories, applicable to nonequilibrium steady states.

Contribution

It introduces a consistent thermodynamic description along single stochastic trajectories, including energy balance, entropy production, and fluctuation relations for reaction networks.

Findings

Derived a first-law energy balance for individual reactions.

Established fluctuation theorems for nonequilibrium networks.

Demonstrated results on a cyclic reaction network with steady states.

Abstract

For chemical reaction networks described by a master equation, we define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction events. A first-law like energy balance relates internal energy, applied (chemical) work and dissipated heat for every single reaction. Entropy production along a single trajectory involves a sum over changes in the entropy of the network itself and the entropy of the medium. The latter is given by the exchanged heat identified through the first law. Total entropy production is constrained by an integral fluctuation theorem for networks arbitrarily driven by time-dependent rates and a detailed fluctuation theorem for networks in the steady state. Further exact relations like a generalized Jarzynski relation and a generalized Clausius inequality are discussed. We illustrate these results for a three-species cyclic reaction network which exhibits nonequilibrium steady states as well as transitions between different steady states.