Universal constraint for efficiency and power of a low-dissipation heat engine

Abstract

The constraint relation for efficiency and power is crucial to design optimal heat engines operating within finite time. We find a universal constraint between efficiency and output power for heat engines operating in the low-dissipation regime. Such constraint is validated with an example of Carnot-like engine. Its microscopic dynamics is governed by the master equation. Based on the master equation, we connect the microscopic coupling strengths to the generic parameters in the phenomenological model. We find the usual assumption of low-dissipation is achieved when the coupling to thermal environments is stronger than the driving speed. Additionally, such connection allows the design of practical cycle to optimize the engine performance.PACS numbers: to be added later arXiv:1802.09806v4 [quant-ph]

Maximum efficiency of low-dissipation heat engines at arbitrary power

“…(7)-(9) corresponding to power in the LD model optimised only with respect to the duration of the isothermal branches, t i . These expressions thus still depend on the distribution of t i between the two isotherms, α [16,58]. In order to get the final results (12)- (14) for COP at maximum power in the LD refrigerator, one thus just needs to further optimise the power (A9) with respect to α.…”

“…With respect to heat engines, this task already gained considerable attention in the literature [2]. Expressions for maximum efficiency at given power were derived for quantum thermoelectric heat engines [56,57], LD heat engines [26,58], MNI heat engines [59], a stochastic heat engine based on an uderdamped harmonic oscillator [60], and using general linear response theory [40]. With respect to refrigerators, the treasury of results for general models is not so overflowing, with a notable exception of results for MNI refrigerators [25].…”

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.…”

Finite-time quantum Otto engine: Surpassing the quasistatic efficiency due to friction

“…Owing to the discovery of the trade-off relation between the power and the efficiency of the engine [13][14][15] as well as the development of the shortcut-to-adiabaticity technique [16], the finite-time quantum heat engine has steadily gathered many attentions, where the working fluid can have coherence without any special bath, such as a squeezed or coherent bath. When Hamiltonians at different times do not commute, a portion of work is used to generate coherence.…”