The transient fluctuation theorem of sample entropy production for general stochastic processes

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The transient fluctuation theorem for stochastic processes was first put forward by D J Searles and D J Evans (1999). In the present paper, it is rigorously proved that the transient fluctuation theorem (TFT) of sample entropy production, which is previously defined by Jiang et al (2003) and Reid et al (2005) and also called the general action functional up to boundary terms by Lebowitz and Spohn (1999), holds for general stochastic processes without the assumption of Markovian, homogeneous or stationary properties. Then the condition of our theorem is verified for various stochastic processes, including homogeneous, inhomogeneous Markov chains and general diffusion processes. Among these cases, the transient fluctuation theorems for inhomogeneous Markov chains and general diffusion processes are rigorously derived for the first time.