The role of conservation laws in Stochastic Thermodynamics


Starting from the most general formulation of stochastic thermodynamics—i.e. a thermodynamically consis- tent nonautonomous stochastic dynamics describing systems in contact with several reservoirs—, we define the procedure to identify the conservative and the minimal set of nonconservative contributions in the entropy production. The former is expressed as the difference between changes caused by time-dependent drivings and a generalized potential difference. The latter is a sum over the minimal set of flux-forces controlling the dissipative flows across the system. When the system is initially prepared at equilibrium (e.g. by turning off drivings and forces), a finite-time detailed fluctuation theorem holds for the different contributions. Our approach relies on identifying the complete set of conserved quantities and can be viewed as the extension of generalized Gibbs ensemble theory to nonequilibrium situations.