In this chapter, we consider the stochastic aspects of thermodynamics of feedback control, by taking into account the fluctuations of thermodynamic quantities and information contents. In particular, we generalize the nonequilibrium equalities such as the fluctuation theorem and the Jarzynski equalities to feedback-controlled classical stochastic systems [1, 2], which is the third main part of this thesis. This topic is related to the paradox of Maxwell’s demon [3, 4, 5, 6, 7], and has been a topic of active researches in terms of modern nonequilibrium statistical mechanics [1, 2, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]. In Sect. 9.1, we formulate measurements on nonequilibrium systems. In Sect. 9.2, we formulate the effect of feedback control. In Sect. 9.3, we derive the main results in this chapter, which are the generalized nonequilibrium equalities. In Sect. 9.4, we discuss two typical examples that illustrate our general results.
Mutual Information Feedback Control Entropy Production Leibler Divergence Fluctuation Theorem
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