**Congjie Ou 1, Yuho Yokoi <sup>2</sup> and Sumiyoshi Abe 1,2,3,4,\***


Received: 21 March 2019; Accepted: 6 May 2019; Published: 17 May 2019

**Abstract:** A general comment is made on the existence of various baths in quantum thermodynamics, and a brief explanation is presented about the concept of weak invariants. Then, the isoenergetic process is studied for a spin in a magnetic field that slowly varies in time. In the Markovian approximation, the corresponding Lindbladian operators are constructed without recourse to detailed information about the coupling of the subsystem with the environment called the energy bath. The entropy production rate under the resulting Lindblad equation is shown to be positive. The leading-order expressions of the power output and work done along the isoenergetic process are obtained.

**Keywords:** quantum thermodynamics of spin; weak invariants; isoenergetic process; Lindblad equation
