Geometrical expression of excess entropy production

We derive a geometrical expression of the excess entropy production for quasistatic transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct the thermodynamics of nonequilibrium steady states.

Figure 1

(a) Schematic of the model of a quantum dot. A single electron is transferred to and from the two heat baths with chemical potentials ${\mu }_L$ and ${\mu }_R$. (b) ${\langle \sigma \rangle }_{\mathrm{ex}}$ (solid line) and $-\Delta S$ (dashed line) for quasistatic processes. They are coincident with each other up to second order of the nonequilibrium of the final state, which is denoted by $u$.