The Second Laws for Quantum and Nano-scale Heat Engines

Mohit Lal Bera, Maciej Lewenstein, Manabendra Nath Bera

Published 2019-11-16Version 1

The second law in thermodynamics dictates which state transformations are statistically unlikely or effectively forbidden. However, the statistical formulation of the second law assumes the asymptotic regime, where a system of an asymptotically large number of particles interacts with the thermal baths. In addition, standard thermodynamics relies on mean values of thermodynamic quantities and admits thus the possibility of repeated measurements. This formulation cannot be automatically extended to the finite-size regime, where the system is composed of a small number of particles, let alone that these particles could be of quantum nature and that only one-shot measurement is allowed. In this work, we consider heat engines operating in the finite-size regime and allowed to access one-shot measurements, i.e., the engines are made up of a system with a finite or a small number of quantum particles and two baths at different temperatures, and convert heat into work. We introduce generalized engine operations, the semi-local thermal operations, where the system simultaneously interacts with two baths at different temperatures. We develop a resource theoretic formalism and show that, unlike in the asymptotic regime, thermodynamics of these quantum heat engines is fundamentally irreversible, and it requires many second laws to characterize the state transformations. We construct heat engines that operate with a one-step cycle. These engines improve the one-shot engine efficiency, compared to the engines operating with local thermal operations. Also, they can operate by exclusively exploiting the correlations present in the system. We formulate the statements of various forms of second laws such as one-shot Clausius, Kelvin-Planck, and Carnot statements in the finite-size regime.