Thermodynamics of Gambling Demons

Abstract

We introduce and realize demons that follow a customary gambling strategy to stop a nonequilibrium process at stochastic times. We derive second-law-like inequalities for the average work done in the presence of gambling, and universal stopping-time fluctuation relations for classical and quantum nonstationary stochastic processes. We test experimentally our results in a single-electron box, where an electrostatic potential drives the dynamics of individual electrons tunneling into a metallic island. We also discuss the role of coherence in gambling demons measuring quantum jump trajectories.

Quantum thermodynamics under continuous monitoring: a general framework

“…Very recently, a new decomposition of the entropy production has been proposed based on an extension of the so-called Martingale theory for entropy production [176][177][178][179][180] to quantum trajectories 98,99 . Although we will not discuss here Martingale theory for entropy production, we can fully introduce this decomposition of entropy production with the elements at hand.…”

“…The decomposition of the entropy production is based on a different notion of the entropy of the system as given by the logarithm of the quantum fidelity between the density operator ρ τ of the average dynamics and the stochastic wave function given by the SSE |ψ γ (τ) just prior to the final application of the projectors {Π τ n }. That is 98,99 :…”

“…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] . Recently, the framework has been also used to obtain generalized versions of the Thermodynamic Uncertainty Relations (TUR) [94][95][96][97] that establish trade-off relations between the fluctuations of observable currents and dissipation-and to develop a Quantum Maringale Theory (QMT) describing the thermodynamics of processes at stopping times (such as first-passage times or escape times) in connection to quantum features 98,99 .…”

Gibbs Distribution from Sequentially Predictive Form of the Second Law

“…The martingale property is useful to investigate the statistics at stopping times and extreme value statistics. In the context of nonequilibrium thermodynamics, the novel statistical properties of stochastic entropy production were recently studied [16][17][18][19] based on this property of martingales and the fact that the exponentiated negative entropy production or its modification is a martingale. Although our results are also based on the fact that the exponential of the accumulation of the extracted work is a martingale 2 , we use another property that was first found by Jean Ville [20], the characterization of almost sure properties in terms of martingales.…”

“…In externally driven systems, the exponentiated negative entropy production in a time interval is not martingale in general[16,18,19]. In this paper, however, we do not consider the stochastic time evolution of the system explicitly and concentrate our interest on the sum of the extracted work obtained from statistically independent experiments.…”