Conservation Laws Shape Dissipation

Starting from the most general formulation of stochastic thermodynamics—i.e. a thermodynamically
consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs
—we define a 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-force contributions 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 the theory of generalized
Gibbs ensembles to nonequilibrium situations.