Stochastic thermodynamics of quantum jumps: entropy production, martingales and inefficient detection

Abstract

The thermodynamics of quantum systems driven out of equilibrium has attracted increasing attention in the last decade, in connection with quantum information and statistical physics, and with a focus on non-classical signatures. While a first approach can deal with average thermodynamics quantities over ensembles, in order to establish the impact of quantum and environmental fluctuations during the evolution, a continuous quantum measurement of the open system is required. Such a framework has been developed during the last decade, with recent advances incorporating multiple conserved quantities, the assessment of thermodynamic quantities at stopping times using martingale theory, and the consideration of imperfect and partial monitoring schemes. These advances provide new universal relations in the form of fluctuation theorems and inequalities that refine our understanding of the second-law of thermodynamics in different senses.