Large deviation theory to model systems under an external feedback

TL;DR

This paper develops a large deviation framework incorporating information theory to model systems under external feedback, establishing bounds on entropy reduction and defining new potentials for optimal information use.

Contribution

It introduces a novel large deviation approach combined with rate distortion theory to analyze feedback-controlled systems and defines new thermodynamic-like potentials involving information.

Findings

Bounds on maximum entropy reduction with feedback accuracy

Definition of new potentials including information measures

Framework for optimal use of feedback information

Abstract

In this paper we address the problem of systems under an external feedback. This is performed using a large deviation approach and rate distortion from information theory. In particular we define a lower boundary for the maximum entropy reduction that can be obtained using a feedback apparatus with a well defined accuracy in terms of measurement of the state of the system. The large deviation approach allows also to define a new set of potentials, including information, which similarly to more conventional thermodynamic potentials can define the state with optimal use of the information given the accuracy of the feedback apparatus.