The second law of thermodynamics under unitary evolution and external operations

Journal Article · Sun Mar 15 04:00:00 EDT 2015 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2015.01.003· OSTI ID:22447609

Sakumichi, Naoyuki ^[1]; Polkovnikov, Anatoli ^[2]; Ueda, Masahito ^[3]

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1. Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama 351-0198 (Japan)
2. Physics Department, Boston University, Boston, MA 02215 (United States)
3. Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan)

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.

• OSTI ID: 22447609
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 354; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ENTROPY
EQUILIBRIUM
HAMILTONIANS
PURE STATES
QUANTUM SYSTEMS
STATISTICAL MECHANICS
THERMODYNAMICS
TRAJECTORIES