Chapter 17 delves into quantum thermodynamics, building on the concepts introduced in the resource theory of nonuniformity. This chapter focuses on thermal states and athermality as resources within the quantum domain, emphasizing the significance of Gibbs states and their role in quantum statistical mechanics. It outlines the operational framework for thermal operations, setting the stage for discussions on energy conservation and the second law of thermodynamics in quantum systems. A key aspect of the chapter is the exploration of quasi-classical athermality, illustrating how quantum states deviate from thermal equilibrium when the state of the system commutes with its Hamiltonian. In the fully quantum domain, the chapter introduces closed formulas for quantifying athermality, such as the athermality cost and distillable athermality, both in the single-shot and the asymptotic domains. These measures provide a quantitative understanding of the efficiency of thermal operations and the potential for work extraction or consumption.

Chapter 16, centered on the resource theory of nonuniformity, serves as an essential precursor to discussions on thermodynamics as a resource theory. It presents nonuniformity as a fundamental quantum resource, using it as a toy model to prepare for more complex thermodynamic concepts. In this model, free states are considered to be maximally mixed states, analogous to Gibbs states with a trivial Hamiltonian, providing a simplified context for exploring quantum thermodynamics. The chapter carefully outlines how nonuniformity is quantified, offering closed formulas for the conversion distance, nonuniformity cost, and distillable nonuniformity. These measures are explored both in the single-shot and the asymptotic domains. The availability of closed formulas makes this model particularly insightful, demonstrating clear, quantifiable relationships between various measures of nonuniformity.