Maximum efficiency of low-dissipation heat engines at arbitrary power

Abstract

We investigate maximum efficiency at a given power for low-dissipation heat engines. Close to maximum power, the maximum gain in efficiency scales as a square root of relative loss in power and this scaling is universal for a broad class of systems. For the low-dissipation engines, we calculate the maximum gain in efficiency for an arbitrary fixed power. We show that the engines working close to maximum power can operate at considerably larger efficiency compared to the efficiency at maximum power. Furthermore, we introduce universal bounds on maximum efficiency at a given power for low-dissipation heat engines. These bounds represent direct generalization of the bounds on efficiency at maximum power obtained by Esposito et al. Phys. Rev. Lett. 105, 150603 (2010). We derive the bounds analytically in the regime close to maximum power and for small power values. For the intermediate regime we present strong numerical evidence for the validity of the bounds.

Optimal Cycles for Low-Dissipation Heat Engines

“…Combining recent insights on the maximal power for a fixed efficiency of LD heat engines [8,9] with a geometrical approach to (quantum) thermodynamics [18][19][20][21][22][23][24][25][26][27][28], we show that, given any reasonable figure of merit involving power and efficiency, the optimal control strategy is always to perform infinitesimal Carnot-cycles around a fixed point. Furthermore, when the thermalization of the relevant quantities can be described by a single time-scale τ eq (see details below), the optimal power output becomes proportional * paolo.abiuso@icfo.eu to C/τ eq , where C is the heat capacity of the working substance (WS).…”

“…In this article, we consider the optimization of a finite-time Carnot cycle within the so called low-dissipation (LD) regime [3][4][5][6][7][8][9][10][11][12][13][14], where the dissipation is inversely proportional to the time of the process (this corresponds to considering only first-order corrections to the ideal quasistatic limit). Previous studies of Carnot engines in the LD regime have considered bounds on the reachable efficiencies [3], tradeoffs between efficiency and power [7][8][9]15], the coefficient of performance of refrigerators [12,13], the impact of the spectral density of the thermal baths [14], and other thermodynamic figures of merit [10,11]. Despite this remarkable progress, the following crucial question has remained unaddressed: given a certain level of control on the working substance (e.g.…”

Carnot-Like Heat Engines Versus Low-Dissipation Models

“…The nature of the dissipations (entropy generation) are encompassed in some generic dissipative coefficients, so that the optimization of power output (or any other figure of merit) is made easily through the contact times of the engine with the hot and cold reservoirs [36][37][38][39]. In this way, depending on the symmetry of the dissipative coefficients, it is possible to recover several results of the CA-model.…”

Performance optimization of low-dissipation thermal machines revisited

“…Because of its simplicity, the low-dissipation model has attracted a lot of attention [10][11][12][13][14][15][16][17][18]. Furthermore, there is no explicit requirement on the form of heat-transfer law, or the temperature difference between the heat reservoirs to be small, unlike in endoreversible models [7].…”