Abstract
In this chapter, we review thermodynamics of classical stochastic systems, which has been referred to as stochastic thermodynamics [1–3]. In particular, we discuss nonequilibrium equalities such as the fluctuation theorem and the Jarzynski equality, which lead to the second law of thermodynamics as a corollary. These equalities have been theoretically derived in various setups [4–20] and experimentally verified by using small thermodynamic systems such as macromolecules [21, 22]. First, we formulate the general statement of the detailed fluctuation theorem and discuss its consequences. Second, we derive the detailed fluctuation theorem in Hamiltonian systems and Markovian stochastic systems.
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