Entropy production in continuously measured Gaussian quantum systems

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.

Charging a quantum battery with linear feedback control

“…Similar ideas have been applied to jump-like unravellings of open quantum system dynamics [99][100][101][102]. However, a comprehensive formulation of information thermodynamics along continuous, stochastic trajectories between quantum superposition states appears to be considerably more elusive, notwithstanding some notable recent progress [56][57][58][103][104][105]. Entropic considerations aside, any serious thermodynamic account of a putative quantum battery should include the energy needed for work extraction [106], not to mention the power consumption of the classical control apparatus, which typically exceeds quantum scales by dozens of orders of magnitude.…”

Quantum thermodynamics under continuous monitoring: a general framework

“…In Ref. 80 this approach was used to single out the entropy flux to the environment and the information rate gathered by the continuous monitoring process, hence extending the Sagawa-Ueda second-law inequality with information beyond discrete measurements for Gaussian systems, which was experimentally tested in an optomechanical setup 81 .…”

“…[55][56][57][58] . Contributions from several groups within the community working in quantum thermodynamics [59][60][61][62][63][64][65][66][67][68][69][70][71][72] generalized and tested the framework in the last 8 years, including extensions to scenarios with feedback control [73][74][75][76][77] , diffusive noise 66,[78][79][80][81] and arbitrary environments 68 . Applications to quantum heat engines [82][83][84] , probing correlations 85,86 and the erasure of information 87,88 have been proposed, as well as the development of experimental proposals for measuring heat and work along individual trajectories [89][90][91][92][93] .…”

Battery Charging in Collision Models with Bayesian Risk Strategies

“…[ 51 ], which studied the ergotropy that could be extracted from quantum correlations between a system and a single ancilla. Furthermore, it is opposite in spirit to, e.g., continuously monitored systems [ 52 , 53 ], where one uses measurements in the ancillas to learn something about the system [ 54 , 55 , 56 , 57 ]; here we instead use information about the system to learn about the ancillas.…”