Expected Behavior of Quantum Thermodynamic Machines with Prior Information

Abstract

We estimate the expected behavior of a quantum model of heat engine when we have incomplete information about external macroscopic parameters, like magnetic field controlling the intrinsic energy scales of the working medium. We explicitly derive the prior probability distribution for these unknown parameters, $a_i,(i=1,2)$. Based on a few simple assumptions, the prior is found to be of the form $\Pi (a_i)\propto 1/a_i$. By calculating the expected values of various physical quantities related to this engine, we find that the expected behavior of the quantum model exhibits thermodynamic-like features. This leads us to a surprising proposal that incomplete information quantified as appropriate prior distribution can lead us to expect classical thermodynamic behavior in quantum models.

Revtex, 13 pages, 3 figures, revised version, new results added, accepted for Phys. Rev. E

References in corpus (5)

• Efficiency at maximum power of low dissipation Carnot engines
• The second law, Maxwell's daemon and work derivable from quantum heat engines
• Efficiency at maximum power of Feynman's ratchet as a heat engine
• Work extremum principle: Structure and function of quantum heat engines
• Efficiency at maximum power output of linear irreversible Carnot-like heat engines

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• Informative priors and the analogy between quantum and classical heat engines
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