Conservation laws and symmetries in stochastic thermodynamics

Phenomenological nonequilibrium thermodynamics describes how fluxes of conserved quantities, such as
matter, energy, and charge, flow from outer reservoirs across a system and how they irreversibly degrade from
one form to another. Stochastic thermodynamics is formulated in terms of probability fluxes circulating in the
system’s configuration space. The consistency of the two frameworks is granted by the condition of local detailed
balance, which specifies the amount of physical quantities exchanged with the reservoirs during single transitions
between configurations. We demonstrate that the topology of the configuration space crucially determines the
number of independent thermodynamic affinities (forces) that the reservoirs generate across the system and
provides a general algorithm that produces the fundamental affinities and their conjugate currents contributing
to the total dissipation, based on the interplay between macroscopic conservations laws for the currents and
microscopic symmetries of the affinities.