Time Reversal in Doi-Peliti Field Theory for Chemical Reaction Networks

We develop the Doi-Peliti field theoretic description of classical particles undergoing diffusion and chemical reaction, while coupled to thermal and chemical reservoirs. These particles are also subject to a local, time-varying potential, through which work is done on the system. Under the combined effects of time reversal and a gauge-like transformation of the fields, the action for this spatially-extended chemical reaction network is invariant apart from a generated work term. Using this transformation we are able to derive Jarzyski and Crooks relations, as well as a nonequilibrium generalization of the fluctuation-dissipation relation and a heirarchy of additional formal identities.