First and second law of quantum thermodynamics: A consistent derivation based on a microscopic definition of entropy

Deriving the laws of thermodynamics from a microscopic picture is a central quest of statistical mechanics. This tutorial focuses on the derivation of the first and second law for isolated and open quantum systems far from equilibrium, where such foundational questions also become practically relevant for emergent nanotechnologies. The derivation is based on a microscopic definition of five essential quantities: internal energy, thermodynamic entropy, work, heat, and temperature. These definitions are shown to satisfy the phenomenological laws of nonequilibrium thermodynamics for a large class of states and processes. The consistency with previous results is demonstrated. The framework applies to multiple baths including particle transport and accounts for processes with, e.g., a changing temperature of the bath, which is determined microscopically. An integral fluctuation theorem for entropy production is satisfied. In summary, this tutorial introduces a consistent and versatile framework to understand and apply the laws of thermodynamics in the quantum regime and beyond.