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  • Letter

Entropy-based formulation of thermodynamics in arbitrary quantum evolution

S. Alipour1, A. T. Rezakhani2, A. Chenu3,4,5, A. del Campo3,4,5,6, and T. Ala-Nissila1,7

  • 1QTF Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Espoo, Finland
  • 2Department of Physics, Sharif University of Technology, Tehran 14588, Iran
  • 3Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Grand Duchy of Luxembourg
  • 4Donostia International Physics Center, E-20018 San Sebastián, Spain
  • 5IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
  • 6Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
  • 7Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom

Phys. Rev. A 105, L040201 – Published 18 April, 2022

DOI: https://doi.org/10.1103/PhysRevA.105.L040201

Abstract

Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part causing no entropy change, identified as heat and work, respectively. We also demonstrate that heat and work admit geometric and dynamical descriptions by developing a universal dynamical equation for the given trajectory of the system. The dissipative and coherent parts of this equation contribute exclusively to heat and work, where the specific role of a work contribution from a counterdiabatic drive is underlined. Next we define an expression for the irreversible entropy production of the system which does not have explicit dependence on the properties of the ambient environment; rather, it depends on a set of the system's observables excluding its Hamiltonian and is independent of internal energy change. We illustrate our results with three examples.

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