Geometric Bounds on the Power of Adiabatic Thermal Machines

Abstract

We analyze the performance of slowly driven meso-and micro-scale refrigerators and heat engines that operate between two thermal baths with small temperature difference. Using a general scaling argument, we show that such devices can work arbitrarily close to their Carnot limit only if heat-leaks between the baths are fully suppressed. Their power output is then subject to a universal geometric bound that decays quadratically to zero at the Carnot limit. This bound can be asymptotically saturated in the quasi-static limit if the driving protocols are suitably optimized and the temperature difference between the baths goes to zero with the driving frequency. These results hold under generic conditions for any thermodynamically consistent dynamics admitting a well-defined adiabatic-response regime and a generalized Onsager symmetry. For illustration, we work out models of a qubit-refrigerator and a coherent charge pump operating as a cooling device.

Energy dynamics, heat production and heat-work conversion with qubits: towards the development of quantum machines

“…This remarkable different behavior exhibits the relevance of optimizing the protocols in order to reduce the dissipation. These ideas were also used to minimize the dissipation in finite-time Otto and Carnot cycles implemented in qubits [153,154], to analyze the work fluctuations in these systems [155,156], and more recently, to minimize the dissipation in cycles implemented in qubits simultaneously coupled to several reservoirs [157,158].…”

Controlling thermodynamics of a quantum heat engine with modulated amplitude drivings

“…In such driven systems, periodic or nonperiodic modulation of a system parameter (like energy, reservoir temperature etc.) in an adiabatic fashion [17][18][19][20][21] has led to the theoretical prediction of exotic properties such as creating new phases of matter and loss of tunneling a) Electronic mail: hpg@gauhati.ac.in which are corroborated using Floquet theory coupled to adiabatic master equations [21][22][23][24][25] . Further, adiabatic master equations developed by modulating two system parameters have been shown to break nonequilibrium fluctuation theorems and TUR because of the emergence of geometric phaselike quantities 17,[26][27][28][29] .…”

Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems

“…This has enabled finding optimal driving protocols in such regime for complex systems such as a two dimensional Ising model [33,34], nanomagnets [35], and quantum spin chains [36]. Optimal protocols for different classes of slowly driven heat engines have also been developed by such a geometric approach [32,[37][38][39][40][41][42][43][44]. Besides the slow driving regime, the optimization problem can also be simplified in the opposite, fast-driving, regime [45][46][47][48].…”