Weak invariants, temporally local equilibria and isoenergetic processes described by the Lindblad equation

¹ Physics Division, College of Information Science and Engineering, Huaqiao University - Xiamen 361021, China
² ESIEA - 9 Rue Vesale, Paris 75005, France
³ Department of Physical Engineering, Mie University - Mie 514-8507, Japan
⁴ Institute of Physics, Kazan Federal University - Kazan 420008, Russia

Received: 26 January 2019
Accepted: 18 March 2019

Abstract

The concept of weak invariants is examined in the thermodynamic context. Discussions are made about the temporally local equilibrium states, corrections to them, and isoenergetic processes based on the quantum master equations of the Lindblad type that admit time-dependent Hamiltonians as weak invariants. The method for determining the correction presented here may be thought of as a quantum-mechanical analog of the Chapman-Enskog expansion in nonequilibrium classical statistical mechanics. Then, the theory is applied to the time-dependent harmonic oscillator as a simple example, and the power output and the work along an isoenergetic process are evaluated within the framework of finite-time quantum thermodynamics.