  We consider classical, interacting particles coupled to a thermal reservoir
and subject to a local, time-varying potential while undergoing hops on a
lattice. We impose detailed balance on the hopping rates and map the dynamics
to the Fock space Doi representation, from which we derive the Jarzynski and
Crooks relations. Here the local potential serves to drive the system far from
equilibrium and to provide the work. Next, we utilize the coherent state
representation to map the system to a Doi-Peliti field theory and take the
continuum limit. We demonstrate that time reversal in this field theory takes
the form of a gauge-like transformation which leaves the action invariant up to
a generated work term. The time-reversal symmetry leads to a fundamental
identity, from which we are able to derive the Jarzynski and Crooks relations,
as well as a far-from-equilibrium generalization of the fluctuation-dissipation
relation.
