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Entropy production is a key quantity in any finite-time thermodynamicprocess. It is intimately tied with the fundamental laws of thermodynamics,embodying a tool to extend thermodynamic considerations all the way tonon-equilibrium processes. It is also often used in attempts to provide thequantitative characterization of logical and thermodynamic irreversibility,stemming from processes in physics, chemistry and biology. Notwithstanding itsfundamental character, a unifying theory of entropy production valid forgeneral processes, both classical and quantum, has not yet been formulated.Developments pivoting around the frameworks of stochastic thermodynamics, openquantum systems, and quantum information theory have led to substantialprogress in such endeavour. This has culminated in the unlocking of a newgeneration of experiments able to address stochastic thermodynamic processesand the impact of entropy production on them. This paper aims to provide acompendium on the current framework for the description, assessment andmanipulation of entropy production. We present both formal aspects of itsformulation and the implications stemming from the potential quantum nature ofa given process, including a detailed survey of recent experiments.

Irreversible entropy production, from quantum to classical