  In these decades, it has been revealed that there is rich
information-theoretic structure in thermodynamics of out-of-equilibrium systems
in both the classical and quantum regimes. This has led to the fruitful
interplay among statistical physics, quantum information theory, and
mathematical theories including matrix analysis and asymptotic probability
theory. The main purpose of this book is to clarify how information theory
works behind thermodynamics and to shed modern light on it. We focus on both of
purely information-theoretic concepts and their physical implications: We
present self-contained and rigorous proofs of several fundamental properties of
entropies, divergences, and majorization. We also discuss the modern
formulations of thermodynamics, especially from the perspectives of stochastic
thermodynamics and resource theory of thermodynamics. Resource theory is a
recently-developed field as a branch of quantum information theory in order to
quantify (energetically or information-theoretically) "useful resources." We
show that resource theory has an intrinsic connection to various fundamental
ideas of mathematics and information theory. This book is not intended to be a
comprehensive review of the field, but would serve as a concise introduction to
several important ingredients of the information-theoretic formulation of
thermodynamics.
