Efficiency at maximum power of minimally nonlinear irreversible heat engines

Abstract

-We propose the minimally nonlinear irreversible heat engine as a new general theoretical model to study the efficiency at the maximum power η * of heat engines operating between the hot heat reservoir at the temperature T h and the cold one at Tc (Tc ≤ T h ). Our model is based on the extended Onsager relations with a new nonlinear term meaning the power dissipation. In this model, we show that η * is bounded from the upper side by a function of the Carnot efficiencyWe demonstrate the validity of our theory by showing that the low-dissipation Carnot engine can easily be described by our theory.

Efficiency at and near maximum power of low-dissipation heat engines

“…Our main results are Eqs. (34) and (35) which demonstrate that any trade-off measure expressible in terms of efficiency η and the ratio P/P ⋆ of power to its maximum value exhibits the same degree of universality as the EMP. Consequently, for many systems the tradeoff measure can be optimized independently of most details of the dynamics and of the coupling to thermal reservoirs.…”

“…Namely a general expression for the EMP for these engines has been published [15] and subsequently lower and upper bounds on the EMP were derived [29]. All these results have been confirmed within a minimally nonlinear irreversible thermodynamics framework [34,35]. Another universal result recently appeared in the realm of Brownian motors [36][37][38][39].…”

Geometric phaselike effects in a quantum heat engine

“…(3b). We further observe that the EMP is not restrictive in the bounds η c /2 ≤ η * ≤ η c /(2 − η c ) [28,29] as seen from Fig. (3b).…”

“…Close to equilibrium in the endo-reversible regime, η * = η c /2 + η 2 c /8, with the coefficient 1/2 being universal [25][26][27]. Further it is also known that the efficiency at maximum power is bounded above and below by η c /2 ≤ η * ≤ η c /(2 − η c ) [28,29]. In this work, we show that this strong standing linear expansion coefficient, 1/2, doesn't hold due to the emergence of PBp effects and one can go both above and below the upper bound on η * by having phase different driving protocols.…”

Unified Approach to Thermodynamic Optimization of Generic Objective Functions in the Linear Response Regime

“…The definitions of J 1 and X 1 typically depend on the specific model in question [20], however, no matter how they are defined, we can formally write…”