Stochastic thermodynamic engines under time-varying temperature profile

Abstract

A recently developed stochastic control formalism (Stochastic Thermodynamics) has opened for the first time the possibility to quantify energy exchange and entropy production in finite-time thermodynamic transitions, based on Langevin models for mesoscopic thermodynamic systems. Within this framework we quantify power output and efficiency of overdamped stochastic thermodynamic engines that are powered by a heat bath with temperature that varies periodically with time. Our setting is in contrast to most of the existing literature that considers the Carnot paradigm, alternating contact with heat baths having different fixed temperatures, hot and cold. Specifically, we consider a periodic and bounded but otherwise arbitrary temperature profile and derive explicit bounds on the power and efficiency achievable by a suitably controlling potential that couples the thermodynamic engine to the external world – the time-varying potential represents the control input to the system. A standing assumption in our analysis is that the norm of the gradient of the potentials is bounded – in the absence of any such constraint on the control input, the physically questionable conclusion of arbitrarily large power can be drawn.