Stochastic efficiency of thermodiffusion: an extended local equilibrium approach

Abstract

The recently established connection between stochastic thermodynamics and fluctuating hydrodynamics is applied to a study of efficiencies in the coupled transport of heat and matter on a small scale. A stochastic model for a mesoscopic cell connected to two macroscopic reservoirs of heat and particles is developed, based on fluctuating hydrodynamics. Within this approach, the fluctuating separation and thermodynamic efficiencies are defined. The conditions required to observe bimodal distributions of these efficiencies are determined, and the evolution of these distributions is investigated in the large-size and in the long-time limits. The results obtained are not restricted to thermodiffusion and can be generalized to systems where efficiency is defined as a ratio of stochastic state variables or dissipation rates.

Stochastic thermodynamics: experiment and theory

“…They study distribution of two types of efficiency (separation and thermodynamic efficiencies) in this process, and in particular the condition for having a bimodal distribution of efficiency. Theoretical results are supplemented by a vast amount of numerical simulations which highlight the universality of the theory, applicable also to stochastic efficiencies of ratios of dissipations used in Carnot cycles or the ratio of electrical and heat fluxes in fuel cells [9,10].…”

An autonomous out of equilibrium Maxwell's demon for controlling the energy fluxes produced by thermal fluctuations

“…The Demon efficiency can be defined in two ways. As the demon does not exchange any work and heat with the system then the efficiency can be defined in terms of entropy production rates, which has been used in other contexts [23][24][25]. Another way to define efficiency is in terms of the energy fluxes.…”