Irreversibility in a unitary finite-rate protocol: the concept of internal friction

Abstract

Abstract. The concept of internal friction, a fully quantum mechanical phenomena, is investigated in a simple, experimentally accessible quantum system in which a spin-1/2 is driven by a transverse magnetic field in a quantum adiabatic process. The irreversible production of the waste energy due to the quantum friction is quantitatively analyzed in a forward-backward unitary transform of the system Hamiltonian by using the quantum relative entropy between the actual density matrix obtained in a parametric transformation and the one in a reversible adiabatic process. Analyzing the role of total transformation time and the different pulse control schemes on the internal friction reveal the non-monotone character of the internal friction as a function of the total protocol time and the possibility for almost frictionless solutions in finite-time transformations. IntroductionRecent advances in nanotechnology enable successful fabrication and control of systems in length scales where quantum features and fluctuations are dominant. If we are to use these quantum systems for useful purposes, such as heat to work conversion (i.e, as a quantum heat engine), we have to deal with the limitations imposed by quantum mechanics, such as quantum friction, on the thermodynamical transformations and cycles [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. Quantum friction is the hallmark of finite-time thermodynamical transformations. The infinitely long lasting ones are the reversible processes, which can drive the quantum systems from an equilibrium state to the another one. Reversible processes are, in general, optimal for the work output and the operational efficiency of the quantum heat engines, but they are in the expense of power output. For better powered quantum engines, one typically requires faster thermodynamical transformations, which are irreversible and drive the system outside of equilibrium states, leading to (unwanted) entropy production.

Work production of quantum rotor engines

“…In both models, we observe that the work accumulation eventually slows down. Indeed, it is not uncommon that the output power of an engine decreases with fast operating cycles [47][48][49][50][51][52], and we have seen in figures 2 and 3 that there exists a point of maximum power beyond which the work rate starts to fall. The critical cycle duration is determined by the finite reaction time of the working fluid, here reached when k á ñL I .…”

Performance of a quantum heat engine at strong reservoir coupling

“…It is well known that operating the cycle in the sudden limit introduces a process known as quantum friction [17,58], which impacts negatively on the performance of the engine. This is apparent, for instance, in Fig.…”

Irreversible work and internal friction in a quantum Otto cycle of a single arbitrary spin

“…The erased information-coherence as a heat may find correspondence through the interpretation of Landauer's principle [60]. We should stress here that the excess work, being quantum or classical in origin, for isolated quantum systems and its non-monotonic feature as a function of switching time have also been discussed in different contents [55][56][57].…”