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Register a new userQuantum mechanical bound for efficiency of quantum Otto heat engine
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The second law of thermodynamics constrains that the efficiency of heat engines, classical or quantum, cannot be greater than the universal Carnot efficiency. We discover another bound for the efficiency of a quantum Otto heat engine consisting of a harmonic oscillator. Dynamics of the engine is governed by the Lindblad equation for the density matrix, which is mapped to the Fokker-Planck equation for the quasi-probability distribution. Applying stochastic thermodynamics to the Fokker-Planck equation system, we obtain the $hbar$-dependent quantum mechanical bound for the efficiency. It turns out that the bound is tighter than the Carnot efficiency. The engine achieves the bound in the low temperature limit where quantum effects dominate. Our work demonstrates that quantum nature could suppress the performance of heat engines in terms of efficiency bound, work and power output.
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In finite-time quantum heat engines, some work is consumed to drive a working fluid accompanying coherence, which is called `friction. To understand the role of friction in quantum thermodynamics, we present a couple of finite-time quantum Otto cycles with two different baths: Agarwal versus Lindbladian. We solve them exactly and compare the performance of the Agarwal engine with that of the Lindbladian engine. In particular, we find remarkable and counterintuitive results that the performance of the Agarwal engine due to friction can be much higher than that in the quasistatic limit with the Otto efficiency, and the power of the Lindbladian engine can be nonzero in the short-time limit. Based on additional numerical calculations of these outcomes, we discuss possible origins of such differences between two engines and reveal them. Our results imply that even with an equilibrium bath, a nonequilibrium working fluid brings on the higher performance than what an equilibrium working fluid does.
We derive the probability distribution of the efficiency of a quantum Otto engine. We explicitly compute the quantum efficiency statistics for an analytically solvable two-level engine. We analyze the occurrence of values of the stochastic efficiency above unity, in particular at infinity, in the nonadiabatic regime and further determine mean and variance in the case of adiabatic driving. We finally investigate the classical-to-quantum transition as the temperature is lowered.
We derive the general probability distribution function of stochastic work for quantum Otto engines in which both the isochoric and driving processes are irreversible due to finite time duration. The time-dependent power fluctuations, average power, and thermodynamic efficiency are explicitly obtained for a complete cycle operating with an analytically solvable two-level system. We show that, there is a trade-off between efficiency (or power) and power fluctuations.
We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two non-interacting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.
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