Entropy production is a key quantity in any finite-time thermodynamic process. It is intimately tied with the fundamental laws of thermodynamics, embodying a tool to extend thermodynamic considerations all the way to nonequilibrium processes. It is also often used in attempts to provide the quantitative characterization of logical and thermodynamic irreversibility, stemming from processes in physics, chemistry, and biology. Notwithstanding its fundamental character, a unifying theory of entropy production valid for general processes, both classical and quantum, has not yet been formulated. Developments pivoting around the frameworks of stochastic thermodynamics, open quantum systems, and quantum information theory have led to substantial progress in such endeavors. This has culminated in the unlocking of a new generation of experiments able to address stochastic thermodynamic processes and the impact of entropy production on them. This review aims to provide a compendium on the current framework for the description, assessment, and manipulation of entropy production. Formal aspects of its formulation and the implications stemming from the potential quantum nature of a given process, including a detailed survey of recent experiments, are both presented.

We report the experimental reconstruction of the nonequilibrium work probability distribution in a closed quantum system, and the study of the corresponding quantum fluctuation relations. The experiment uses a liquid-state nuclear magnetic resonance platform that offers full control on the preparation and dynamics of the system. Our endeavors enable the characterization of the out-of-equilibrium dynamics of a quantum spin from a finite-time thermodynamics viewpoint.

The practical untenability of the quasi-static assumption makes any realistic engine intrinsically irreversible and its operating time finite, thus implying friction effects at short cycle times. An important technological goal is thus the design of maximally efficient engines working at the maximum possible power. We show that, by utilising shortcuts to adiabaticity in a quantum engine cycle, one can engineer a thermodynamic cycle working at finite power and zero friction. Our findings are illustrated using a harmonic oscillator undergoing a quantum Otto cycle.

We propose an interferometric setting for the ancilla-assisted measurement of the characteristic function of the work distribution following a time-dependent process experienced by a quantum system. We identify how the configuration of the effective interferometer is linked to the symmetries enjoyed by the Hamiltonian ruling the process and provide the explicit form of the operations to implement in order to accomplish our task. We finally discuss two physical settings, based on hybrid optomechanical-electromechanical devices, where the theoretical proposals discussed in our work could find an experimental demonstration.