Detailed Fluctuation Relation for Arbitrary Measurement and Feedback Schemes

Abstract

Fluctuation relations are powerful equalities that hold far from equilibrium. However, the standard approach to include measurement and feedback schemes may become inapplicable in certain situations, including continuous measurements, precise measurements of continuous variables, and feedback induced irreversibility. Here we overcome these shortcomings by providing a recipe for producing detailed fluctuation relations. Based on this recipe, we derive a fluctuation relation which holds for arbitrary measurement and feedback control. The key insight is that fluctuations inferable from the measurement outcomes may be suppressed by post-selection. Our detailed fluctuation relation results in a stringent and experimentally accessible inequality on the extractable work, which is saturated when the full entropy production is inferable from the data. arXiv:1807.05034v2 [cond-mat.mes-hall]

Work estimation and work fluctuations in the presence of non-ideal measurements

“…Conceptually, our results can be seen as a constructive resolution of the perceived shortcomings of the TPM discussed in [65]. It might also be interesting to consider work estimates as well as Jarzynski's equality and Crooks' theorem in more general contexts, such as including feedback control strategies [69,70].…”

Colloidal engines for innovative tests of information thermodynamics

“…By directly controlling and measuring the mutual information passing through the noisy detector, the colloidal information engines discussed here fully characterized the information-energy interplay over a wide variety of non-equilibrium steady states and verified the generalized second law and integral fluctuation theorems. The more general fluctuation theorems valid for systems under arbitrary measurement and feedback control, such as the fluctuation theorems for total entropy production [62], or the generalized detailed fluctuation theorems [15], which require the measurement of the heat, entropy, and mutual information along individual forward and backward trajectories, are yet to be verified experimentally. Most studies in information thermodynamics mainly focus on resolving the paradox imposed by Maxwell's demon, where entropy production and mutual information between the system and the demon are treated on an equal footing.…”

“…The past decade witnessed significant advances in the field of information thermodynamics that incorporate stochastic thermodynamics [8,9] and fluctuation theorems [10,11,12]. The general theoretical frameworks, which generalizes the fluctuation theorems and the second laws of stochastic thermodynamics for the system in presence of correlation, and information processing such as feedback control and information erasure, were formulated [13][14][15][16]. Also, various models for 'Maxwell's demon' type information engines, capable of extracting work from a single heat bath by utilizing information about the microscopic state of the system, were developed [17,18,19,20,21].…”

Thermodynamic uncertainty relations including measurement and feedback

“…Here we consider the fluctuation relation put forward in Ref. [39]. The probability distribution for this backward experiment (see main text for details) reads…”

“…In its most common version, the backward experiment is obtained by time-reversing the forward experiment, φ is an observable that is odd under time-reversal, and σ I denotes the entropy production [1]. There are numerous extensions of the fluctuation relation, illustrating the fact that different choices for the backward experiment result in different extensions of σ I , each with its own interpretation and merits [1,[37][38][39][40]. Here we focus on extensions including measurement and feedback, where σ I includes an information term symbolized by the subscript I [14,39,.…”