Smoothed generalized free energies for thermodynamics

Abstract

In the study of thermodynamics for nanoscale quantum systems, a family of quantities known as generalized free energies have been derived as necessary and sufficient conditions that govern state transitions. These free energies become important especially in the regime where the system of interest consists of only a few (quantum) particles. In this work, we introduce a new family of smoothed generalized free energies, by constructing explicit smoothing procedures that maximize/minimize the free energies over an $\epsilon$-ball of quantum states. In contrast to previously known smoothed free energies, these quantities now allow us to make an operational statement for approximate thermodynamic state transitions. We show that these newly defined smoothed quantities converge to the standard free energy in the thermodynamic limit.

arXiv comment6 pages main text + 12 pages appendix, revised version with new figure and corollary, results unchanged

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• Collective operations can extremely reduce work fluctuations
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• Optimal common resource in majorization-based resource theories
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• Quantum entanglement shared in hydrogen bonds and its usage as a resource in molecular recognition
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• Which Bath-Hamiltonians Matter for Thermal Operations?
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