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arXiv:1602.06164 · Physica Scripta

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

Selçuk Çakmak, Ferdi Altintas, Özgür Esat Müstecaplıoğlu

Published Jun 1, 2016• 15 citations
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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.

DOI
10.1088/0031-8949/91/7/075101

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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.
We discuss the thermodynamics of closed quantum systems driven out of equilibrium by a change in a control parameter and undergoing a unitary process. We compare the work actually done on the system with the one that would be performed along ideal adiabatic and isothermal transformations. The comparison with the latter leads to the introduction of irreversible work, while that with the former leads to the introduction of inner friction. We show that these two quantities can be treated on an equal footing, as both can be linked with the heat exchanged in thermalization processes and both can be expressed as relative entropies. Furthermore, we show that a specific fluctuation relation for the entropy production associated with the inner friction exists, which allows the inner friction to be written in terms of its cumulants.
A single spin that is misaligned with respect to the static external magnetic field is investigated as a toy model to clarify the nature of irreversibility in terms of inner friction and irreversible work. The coherence generation and the effects of unwanted transitions are analyzed in detail. The behavior of inner friction and irreversible work as a function of protocol time are analyzed for a finite-time unitary transformation. The coherence generation is shown to be the common sign for the inner friction and irreversible work. The excess energy sourced by the unwanted transitions for a quasistatic transformation is found to be the only sign for irreversible work. The angle The angle dependencies of the inner friction and irreversible work are also analyzed explicitly. The selected model and the considered realistic parameters are available to be implemented for the finite-time operations on the nuclear magnetic resonance setups.
An irreversible cycle model of a quantum heat engine with internal friction is established, which is composed of two adiabatic and two isomagnetic field processes. The working substance of the cycle consists of an ensemble of many non-interacting spin-1/2 systems. Based on a quantum master equation and semi-group approach, the general performance characteristics of the heat engine are investigated. The general expressions for several important parameters, such as the efficiency, power output, and rate of the entropy production, are derived. The performance of the cycle is optimized with respect to the temperatures of the working substance. By numerical solutions, the maximum power output and the corresponding parameters are calculated. The optimal regions of efficiency, temperatures of the working substance, and cycle period are determined. Moreover, the performance of the heat engine in the frictionless case is obtained, which is different from that in the friction case. Finally, the results obtained are generalized to the performance optimization of the heat engine working with spin-J systems.
Abstract One of the major goals of quantum thermodynamics is the characterization of irreversibility and its consequences in quantum processes. Here, we discuss how entropy production provides a quantification of the irreversibility in open quantum systems through the quantum fluctuation theorem. We start by introducing a two-time quantum measurement scheme, in which the dynamical evolution between the measurements is described by a completely positive, trace-preserving (CPTP) quantum map (forward process). By inverting the measurement scheme and applying the time-reversed version of the quantum map, we can study how this backward process differs from the forward one. When the CPTP map is unital, we show that the stochastic quantum entropy production is a function only of the probabilities to get the initial measurement outcomes in correspondence of the forward and backward processes. For bipartite open quantum systems we also prove that the mean value of the stochastic quantum entropy production is sub-additive with respect to the bipartition (except for product states). Hence, we find a method to detect correlations between the subsystems. Our main result is the proposal of an efficient protocol to determine and reconstruct the characteristic functions of the stochastic entropy production for each subsystem. This procedure enables to reconstruct even others thermodynamical quantities, such as the work distribution of the composite system and the corresponding internal energy. Efficiency and possible extensions of the protocol are also discussed. Finally, we show how our findings might be experimentally tested by exploiting the state of-the-art trapped-ion platforms.
In this work we considered the quantum Otto cycle within an optimization framework. The goal was maximizing the power for a heat engine or maximizing the cooling power for a refrigerator. In the field of finite-time quantum thermodynamics it is common to consider frictionless trajectories since these have been shown to maximize the work extraction during the adiabatic processes. Furthermore, for frictionless cycles, the energy of the system decouples from the other degrees of freedom, thereby simplifying the mathematical treatment. Instead, we considered general limit cycles and we used analytical techniques to compute the derivative of the work production over the whole cycle with respect to the time allocated for each of the adiabatic processes. By doing so, we were able to directly show that the frictionless cycle maximizes the work production, implying that the optimal power production must necessarily allow for some friction generation so that the duration of the cycle is reduced.
The concept of inner friction, by which a quantum heat engine is unable to follow adiabatically its strokes and thus dissipates useful energy, is illustrated in an exact physical model where the working substance consists of an ensemble of misaligned spins interacting with a magnetic field and performing the Otto cycle. The effect of this static disorder under a finite-time cycle gives a new perspective of the concept of inner friction under realistic settings. We investigate the efficiency and power of this engine and relate its performance to the amount of friction from misalignment and to the temperature difference between heat baths. Finally we propose an alternative experimental implementation of the cycle where the spin is encoded in the degree of polarization of photons.