Thermodynamics and Steady State of Quantum Motors and Pumps Far from Equilibrium

Abstract

In this article, we briefly review dynamical and thermodynamical aspects of different forms of quantum motors and quantum pumps. We then extend previous results to provide new theoretical tools for a systematic study of those phenomena at far-from-equilibrium conditions. We mainly focus on two key topics: (1) The steady-state regime of quantum motors and pumps, paying particular attention to the role of higher-order terms in the nonadiabatic expansion of the current-induced forces.(2) The thermodynamical properties of such systems, emphasizing systematic ways of studying the relationship between different energy fluxes (charge and heat currents, and mechanical power) passing through the system when beyond-first-order expansions are required. We derive a general order-by-order scheme based on energy conservation to rationalize how every order of the expansion of one form of energy flux is connected with the others. We use this approach to give a physical interpretation of the leading terms of the expansion. Finally, we illustrate the above-discussed topics in a double quantum dot within the Coulomb-blockade regime and capacitively coupled to a mechanical rotor. We find many exciting features of this system for arbitrary nonequilibrium conditions: A definite parity of the expansion coefficients with respect to the voltage or temperature biases; negative friction coefficients; and the fact that, under fixed parameters, the device can exhibit multiple steady states where it may operate as a quantum motor or as a quantum pump depending on the initial conditions.

Bound on Efficiency of Heat Engine from Uncertainty Relation Viewpoint

“…Different models and methods to explain the working principle of the Szilard engine have been explored in various works [ 22 , 23 , 24 , 25 , 26 ]. Various models and working mediums for the analysis of thermal machines has been recently explored in various works [ 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ].…”

Current-induced forces in single-resonance systems

“…Such current-induced forces (CIFs), sometimes dubbed "electron wind forces", have attracted increasing attention in many areas of Condensed Matter physics, including molecular electronics, nanoelectromechanics, 23,24 electromigration, 25,26 and quantum thermodynamics. [27][28][29][30][31][32] Among the most interesting examples are those where the forces are nonconservative. These types of forces may result in phenomena such as cooling, heating, or amplification of mechanical motions.…”

“…This is the reverse of what happens in a quantum pump, where the driving Hamiltonian's parameters, which may arise from a mechanical or an external electrical manipulation, induces a current. 3,6,16,27,29,30,33 Understanding the rules that dictate the interplay between the electronic and the mechanical degrees of freedom is crucial for the design of optimal electromechanical devices, and it can even contribute to the emergence of devices with novel features.…”

“…This is so as quantum motors, quantum pumps, and some nanoelectromechanical devices can be interpreted as macroscopic manifestations of quantum behavior. Thus, these systems may provide new insights into the transition between the classical and quantum worlds, both from a dynamical 9,16 and a thermodynamical [29][30][31][32] perspective. Moreover, the effective Hamiltonian of open quantum systems turns out to be non-Hermitian, which adds an extra richness to the problem.…”

Quantum Transport in Mesoscopic Systems

“…Interestingly, they find that power, efficiency, and fluctuations are bounded by thermodynamic uncertainty relations. Additionally, Bustos, Marún, and Calvo [ 13 ] introduce mechanical degrees of freedom to analyze the dynamics of quantum motors built, e.g., from double quantum dots coupled to rotors. A Langevin approach allows them to generically describe both motors and pumps out of equilibrium, which are relevant for quantum refrigeration setups.…”