Universal bounds on cooling power and cooling efficiency for autonomous absorption refrigerators

Abstract

For steady-state autonomous absorption refrigerators operating in the linear response regime, we show that there exists a hierarchy between the relative fluctuation of currents for cold, hot, and work terminals. Our proof requires the Onsager's reciprocity relation along with the refrigeration condition that sets the direction of the mean currents for each terminal. As a consequence, the universal bounds on the mean cooling power, obtained following the thermodynamic uncertainty relations, receive a hierarchy. Interestingly, within this hierarchy, the tightest bound is given in terms of the work current fluctuation. Furthermore, the relative uncertainty hierarchy hands over additional bounds that can be tighter than the bounds obtained from the thermodynamic uncertainty relations. Interestingly, all of these bounds saturate in the tight-coupling limit. We test the validity of our results for two paradigmatic absorption refrigerator models: (i) a four-level working fluid and (ii) a two-level working fluid, operating, respectively, in the weak (additive) and in the strong (multiplicative) system-bath interaction regime.

Universal bounds on fluctuations for machines with broken time-reversal symmetry

“…[42] that for an autonomous time-reversal symmetric steady-state setup, operating as a useful machine (e.g., engine, refrigerator or pump), the relative fluctuation of output current is always lower bounded by the corresponding relative fluctuation of the input current. As an immediate consequence of this result, a novel upper bound on engine's efficiency was received in terms of the fluctuations of output and input currents which is tighter than the celebrated Carnot bound [27,28,42]. A natural question that immediately arises following the work in Ref.…”

“…Over the past two decades, discoveries of various types of universal fluctuation relations [12][13][14][15][16][17][18][19][20][21] have further enhanced our understanding about thermodynamics of non-equilibrium systems beyond the typical linear response regime. In recent times, intense efforts have been directed towards understanding the impact of fluctuations on small scale non-equilibrium systems and more specifically on the performance of operational machines [21][22][23][24][25][26][27][28]. In this regard, recently discovered thermodynamic uncertainty relations (TURs) [29][30][31][32][33][34][35][36][37][38][39][40][41] have provided new and intriguing insights for autonomous and driven thermal machines by revealing a universal tradeoff type relation involving efficiency, output power and its fluctuation [30][31][32].…”

Is there any upper bound on current fluctuation in cross-transport beyond linear response regime?

“…They also demonstrated the validity of these inequalities beyond the linear response regime by numerical simulations. These inequalities are also verified in cyclic heat engines [37,39] and generalized stationary setups in the linear response regime [40,41].…”

Quantum transport in quasi-periodic lattice systems in presence of Büttiker probes

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