Abstract
The entropy production rate is a key quantity in nonequilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress toward its full grasping. By using a phase space-based approach, here we take the current framework for the assessment of thermodynamic irreversibility all the way to quantum regimes by characterizing entropy production—and its rate—resulting from the continuous monitoring of a Gaussian system. This allows us to formulate a sharpened second law of thermodynamics that accounts for the measurement back action and information gain from a continuously monitored system. We illustrate our framework in a series of physically relevant examples.
Highlights
Entropy production, a fundamental concept in nonequilibrium thermodynamics, provides a measure of the degree of irreversibility of a physical process
The dynamics of a continuously measured Markovian open quantum system can be described by a stochastic master equation (SME) that describes the evolution conditioned on the
The second law of thermodynamics for the unconditional dynamics is encoded in Πuc ≥ 0
Summary
A fundamental concept in nonequilibrium thermodynamics, provides a measure of the degree of irreversibility of a physical process It is of paramount importance for the characterization of an ample range of systems across all scales, from macroscopic to microscopic[1,2,3,4,5,6,7,8,9,10,11]. Its quantification must pass through inference strategies that connect the values taken by such quantity to accessible observables, such as energy[12,13,14] This approach has recently led to the possibility to experimentally measure entropy production in microscopic[15] and mesoscopic quantum systems[16], and opened up intriguing opportunities for its control[17]. Alternative approaches to the quantification of entropy production are based on the ratio between forward and time-reversed path probabilities of trajectories followed by systems undergoing nonequilibrium processes[18,19,20]
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