Work producing reservoirs: Stochastic thermodynamics with generalized Gibbs ensembles

We develop a consistent stochastic thermodynamics for environments composed of thermodynamic reservoirs
in an external conservative force field, that is, environments described by the generalized or Gibbs canonical
ensemble. We demonstrate that small systems weakly coupled to such reservoirs exchange both heat and work
by verifying a local detailed balance relation for the induced stochastic dynamics. Based on this analysis, we
help to rationalize the observation that nonthermal reservoirs can increase the efficiency of thermodynamic heat
engines.