Work and power fluctuations in a critical heat engine

Abstract

We investigate fluctuations of output work for a class of Stirling heat engines with working fluid composed of interacting units and compare these fluctuations to an average work output. In particular, we focus on engine performance close to a critical point where Carnot's efficiency may be attained at a finite power as reported by M. Campisi and R. Fazio [Nat. Commun. 7, 11895 (2016)2041-172310.1038/ncomms11895]. We show that the variance of work output per cycle scales with the same critical exponent as the heat capacity of the working fluid. As a consequence, the relative work fluctuation diverges unless the output work obeys a rather strict scaling condition, which would be very hard to fulfill in practice. Even under this condition, the fluctuations of work and power do not vanish in the infinite system size limit. Large fluctuations of output work thus constitute inseparable and dominant element in performance of the macroscopic heat engines close to a critical point.

Optimal Cycles for Low-Dissipation Heat Engines

“…We have shown that our proposal can be implemented under weaker assumptions w.r.t. a critical Otto cycle [34], and that it can also overcome macroscopic fluctuations [35]. Furthermore, we stress that our proposal is optimal within its regime of validity, which not only enables one to construct specific examples of heat engines working close to η C [33][34][35][38][39][40][41][42], but also to obtain upper bounds on the maximal power/efficiency of a (manybody) heat engine given a certain level of control.…”

“…a critical Otto cycle [34], and that it can also overcome macroscopic fluctuations [35]. Furthermore, we stress that our proposal is optimal within its regime of validity, which not only enables one to construct specific examples of heat engines working close to η C [33][34][35][38][39][40][41][42], but also to obtain upper bounds on the maximal power/efficiency of a (manybody) heat engine given a certain level of control. In this sense, our results should also be compared to exact optimisations of heat engines [43,[58][59][60][61], where the full solution easily becomes too complex or not even computable with the size of the WS.…”

“…We then use these insights to design many-body heat engines that can operate at Carnot efficiency with finite power per constituent of the WS through a supraextensive scaling of C/τ eq (e.g. in a phase transition), in the spirit of [33,34] (see also [34][35][36][37]). We show that the optimal finite-time Carnot cycle leads to milder conditions for the critical exponents of the WS needed to reach Carnot efficiency when compared to [34].…”

Efficiency at the maximum power of the power law dissipative Carnot-like heat engines with non-adiabatic dissipation

“…If we neglect the inner friction, the adiabatic dissipation coefficients, σ a → 0 and σ b → 0, Eqs. (12) and (15) reduces to the earlier results of power law dissipation Carnot like heat engines with instantaneous adiabatic processes [43]. Now, we discuss whether the non-adiabatic dissipation will influence the universal nature of the extreme bounds on the efficiency at maximum power for different cases of symmetric and asymmetric dissipation limits.…”

“…Studies based on sub-linear transport law [16], stochastic thermodynamics [17,18], steady state heat engine [19], electrically charged black hole [20], classical harmonic oscillator under linear response regime [21] and trapped Bose gas in a quantum heat engine [22] showed that the system efficiency approaches η C at finite power. Recent studies based on classical Markov processes [23,24], fluctuation of work and power [25,26], exergy [27], quantum dot model with zero entropy production [28] and information engines [29,30] also proved the attainability of η C at nonzero power.…”