Control and feedback in stochastic thermodynamics

• Main Author: Maitland, Michael
• Published: University of Warwick 2016
• Subjects: 536; QC Physics
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.714941

Stochastic thermodynamics provides a clear definition of entropy production and the framework of fluctuation theorems has allowed many general results to be obtained for nonequilibrium systems. Notably, relationships for work and free energy in nonequilibrium systems as well as second law-like inequalities have been obtained. A recent extension to this framework has been the addition of feedback and the generalisation of the previously obtained inequalities to incorporate information quantities related to control and feedback. In this thesis we contribute to this framework by first providing a close analysis of the nature of `time-reversal' for feedback systems. Time reversal is a key ingredient in the formulation of the fluctuation relationships from which one obtains the nonequilibrium work functions and so we consider how to meaningfully construct a time-reverse conjugate process for a system with feedback and provide a justification for the Sagawa-Ueda fluctuation relation. We then introduce a simple model of a feedback engine and use it to analyse the fluctuation properties of the information flow between the controlled system and the feedback controller. Finally, we focus on the possibilities for feedback and consider a model whereby feedback is enacted symmetrically between two coupled systems and find that such a system has entropy-reducing dynamics. Since the dynamics appear to violate the second law of thermodynamics, we comment on their validity and argue that mutual feedback may be unphysical.