Fast forward approach to stochastic heat engine

Abstract

The fast-forward (FF) scheme proposed by Nakamura (Proc. R. Soc. A 466, 1135 (2010)) in the context of conservative quantum dynamics can reproduce a quasi-static dynamics in an arbitrarily short time. We apply the FF scheme to the classical stochastic Carnot-like heat engine which is driven by a Brownian particle coupled with a time-dependent harmonic potential and working between the high (T h )-and low (Tc)-temperature heat reservoirs. Concentrating on the underdamped case where momentum degree of freedom is included, we find the explicit expressions for the FF protocols necessary to accelerate both the isothermal and thermally-adiabatic processes, and obtain the reversible and irreversible works. The irreversible work is shown to consist of two terms with one proportional to and the other inversely proportional to the friction coefficient. The optimal value of efficiency η at the maximum power of this engine is found to be universal and given by η * = 1 2

Building an irreversible Carnot-like heat engine with an overdamped harmonic oscillator

“…Nevertheless, we have numerically shown that this result remarkably holds for the whole range of temperature ratios, well beyond the asymptotic prediction. This implies that our cycle is a close to optimal choice for building an efficient mesoscopic heat engine, as compared with the theoretical predictions for other constructions [14,18]. Possible venue for future work includes the study of fluctuations, beyond the mean scenario reported here [43,44].…”

“…), and (iii) the efficiency obtained for large dissipation in the recent proposal, using a fast forward approach [18], to build a Carnot-like engine, η…”

“…We employ these finite-time adiabatic processes to build the corresponding adiabatic branches of the irreversible Carnot engine. Therefore, our approach differs from other recent attempts to construct an irreversible Carnot engine [14][15][16][17][18], the limitations of which are discussed in what follows. Specifically, we focus on the respective definitions of "adiabaticity".…”

“…In Refs. [15,17,18], the adiabatic branches are constructed by changing both the temperature of the bath and the stiffness k of the trap but keeping the ratio T 2 /k constant, which is obtained in the underdamped description. Nevertheless, the condition T 2 /k = const.…”