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Title: The second law of thermodynamics under unitary evolution and external operations

Abstract

The von Neumann entropy cannot represent the thermodynamic entropy of equilibrium pure states in isolated quantum systems. The diagonal entropy, which is the Shannon entropy in the energy eigenbasis at each instant of time, is a natural generalization of the von Neumann entropy and applicable to equilibrium pure states. We show that the diagonal entropy is consistent with the second law of thermodynamics upon arbitrary external unitary operations. In terms of the diagonal entropy, thermodynamic irreversibility follows from the facts that quantum trajectories under unitary evolution are restricted by the Hamiltonian dynamics and that the external operation is performed without reference to the microscopic state of the system.

Authors:
 [1];  [2];  [3];  [4];  [1]
  1. Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan)
  2. (United States)
  3. Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama 351-0198 (Japan)
  4. Physics Department, Boston University, Boston, MA 02215 (United States)
Publication Date:
OSTI Identifier:
22447609
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 354; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENTROPY; EQUILIBRIUM; HAMILTONIANS; PURE STATES; QUANTUM SYSTEMS; STATISTICAL MECHANICS; THERMODYNAMICS; TRAJECTORIES

Citation Formats

Ikeda, Tatsuhiko N., E-mail: ikeda@cat.phys.s.u-tokyo.ac.jp, Physics Department, Boston University, Boston, MA 02215, Sakumichi, Naoyuki, Polkovnikov, Anatoli, and Ueda, Masahito. The second law of thermodynamics under unitary evolution and external operations. United States: N. p., 2015. Web. doi:10.1016/J.AOP.2015.01.003.
Ikeda, Tatsuhiko N., E-mail: ikeda@cat.phys.s.u-tokyo.ac.jp, Physics Department, Boston University, Boston, MA 02215, Sakumichi, Naoyuki, Polkovnikov, Anatoli, & Ueda, Masahito. The second law of thermodynamics under unitary evolution and external operations. United States. doi:10.1016/J.AOP.2015.01.003.
Ikeda, Tatsuhiko N., E-mail: ikeda@cat.phys.s.u-tokyo.ac.jp, Physics Department, Boston University, Boston, MA 02215, Sakumichi, Naoyuki, Polkovnikov, Anatoli, and Ueda, Masahito. Sun . "The second law of thermodynamics under unitary evolution and external operations". United States. doi:10.1016/J.AOP.2015.01.003.
@article{osti_22447609,
title = {The second law of thermodynamics under unitary evolution and external operations},
author = {Ikeda, Tatsuhiko N., E-mail: ikeda@cat.phys.s.u-tokyo.ac.jp and Physics Department, Boston University, Boston, MA 02215 and Sakumichi, Naoyuki and Polkovnikov, Anatoli and Ueda, Masahito},
abstractNote = {The von Neumann entropy cannot represent the thermodynamic entropy of equilibrium pure states in isolated quantum systems. The diagonal entropy, which is the Shannon entropy in the energy eigenbasis at each instant of time, is a natural generalization of the von Neumann entropy and applicable to equilibrium pure states. We show that the diagonal entropy is consistent with the second law of thermodynamics upon arbitrary external unitary operations. In terms of the diagonal entropy, thermodynamic irreversibility follows from the facts that quantum trajectories under unitary evolution are restricted by the Hamiltonian dynamics and that the external operation is performed without reference to the microscopic state of the system.},
doi = {10.1016/J.AOP.2015.01.003},
journal = {Annals of Physics},
number = ,
volume = 354,
place = {United States},
year = {Sun Mar 15 00:00:00 EDT 2015},
month = {Sun Mar 15 00:00:00 EDT 2015}
}