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Optimal control of non-equilibrium processes in stochastic thermodynamics
Physicists and Probabilists have been studying the time reversal properties of Markov processes since at least the famous 1931 paper by E Schroedinger "\"Uber die Umkehrung der Naturgesetze". This interest was until the end of the last decade of last century mainly motivated by the quest for a probabilistic interpretation of Quantum Mechanics.
The recent advent of manipulation techniques of nano-systems has brought about a renewed interest in this topic. In particular, it has been shown that a certain functional related to the time reversal of a Markov process can be consistently interpreted as the entropy production during a non-equilibrium classical transformation. This bridge relation between stochastic process theory and physics can be then used to investigate questions such how to drive a system from a thermodynamical state to another while minimizing a given thermodynamic functional.
Stochastic control theory provides then the natural tools to use. We will try to give a pedagogic overview of some recent results in this direction.
Paolo Muratore-Ginanneschi is currently a University Researcher in the mathematics department at the University of Helsinki. His research interests lie in statistical non-equilibrium physics, and applied stochastic processes.