  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 the present paper, 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 etal. 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.
