Abstract
The common saying, that information is power, takes a rigorous form in stochastic thermodynamics, where a quantitative equivalence between the two helps explain the paradox of Maxwell's demon in its ability to reduce entropy. In this letter, we build on earlier work on the interplay between the relative cost and benefits of information in producing work in cyclic operation of thermodynamic engines (by Sandberg et al. 2014). Specifically, we study the general case of overdamped particles in a time-varying potential (control action) in feedback that utilizes continuous measurements (nonlinear filtering) of a thermodynamic ensemble, to produce suitable adaptations of the second law of thermodynamics that involve information.
Highlights
Thermodynamics is the branch of physics which is concerned with the relation between heat and other forms of energy
It was born of the quest to quantify the maximal efficiency of heat engines, i.e., the maximal ratio of the total work output over the total heat input to a thermodynamic system
This was accomplished in the celebrated work of Carnot [1], [2] where, assuming that transitions take place infinitely slowly, it was shown that the maximal efficiency possible is ηC = 1 − Tc/Th (Carnot efficiency), where Th and Tc are the absolute temperatures of two heat reservoirs, hot and cold respectively, with which the heat engine alternates contact
Summary
Thermodynamics is the branch of physics which is concerned with the relation between heat and other forms of energy. The relation between information and work gradually became a central theme of stochastic thermodynamics [6], [7], [8], [9], [10] – a field shaped in the past two decades to study thermodynamic transitions taking place in finite time. Ideas form stochastic control were naturally brought in and the second law was extended to include discrete time measurements [11], as well as continuous ones, both for quantum systems [12] and classical systems under feedback cooling [13], [14].
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