In equilibrium thermodynamics, the Boltzmann entropy serves as a complete thermodynamic potential that characterizes state convertibility in a necessary and sufficient manner. In this talk, I will present our result [1,2] that a complete thermodynamic potential emerges for quantum many-body systems under physically reasonable assumptions, even in out-of-equilibrium and fully quantum situations. Our proof is based on the resource-theoretic formalism of thermodynamics and the quantum ergodic theorem. The complete thermodynamic potential is in general given by a quantity called the spectral divergence rate, while under some assumptions it reduces to the Kullback-Leibler (KL) divergence rate. In addition, I will discuss the case where an auxiliary system called a catalyst is introduced, and show that the KL divergence again serves as a complete thermodynamic potential if a small amount of correlation is allowed between the system and the catalyst .
Prof. Takahiro Sagawa is a professor at the Department of Applied Physics, School of Engineering, The University of Tokyo. He is a theoretical physicist working on nonequilibrium statistical mechanics (especially in small fluctuating systems), quantum measurement, control, and information theory (in open systems).
 P. Faist, T. Sagawa, K. Kato, H. Nagaoka, F. Brandao, Phys. Rev. Lett. 123, 250601 (2019).
 T. Sagawa, P. Faist, K. Kato, K. Matsumoto, H. Nagaoka, F. Brandao, arXiv:1907.05650
 N. Shiraishi, T. Sagawa, Phys. Rev. Lett. 126, 150502 (2021).