A rigorous derivation of nonequilibrium entropy production via the path-integral formalism is presented. Entropy production is defined as the entropy change piled in a heat reservoir as a result of a nonequilibrium thermodynamic process. It is a central quantity by which various forms of the fluctuation theorem are obtained. The two kinds of the stochastic dynamics are investigated: the Langevin dynamics for an even-parity state and the Brownian motion of a single particle. Mathematical ambiguities in deriving the functional form of the entropy production, which depends on path in state space, are clarified by using a rigorous quantum mechanical approach.
We propose an alternative method to compute the entropy production of a classical underdamped nonequilibrium system in a continuous phase space. This approach has the advantage that it is not necessary to distinguish between even and odd-parity variables. We show that the method leads to the same local entropy production as in previous studies while the differential entropy production along a stochastic trajectory turns out to be different. This demonstrates that the differential entropy production in continuous phase space systems is not uniquely defined.
Upper bound for the average entropy production based on stochastic entropy extrema
热力学第二定律，它断言一个组合系统及其环境的平均总熵产生的非负性，是将詹森不等式应用于涨落关系的直接结果。通过这个不等式，也可以根据沿着最极端的随机轨迹的熵来确定平均总熵产生的上界。在这项工作中，我们构造了一个上界不等式的凸函数的平均，其平均是已知的。当应用于各种涨落关系时，建立了平均总熵产生的上界。最后，通过使用Neri，Roldán和Jülicher的结果[Phys. Rev. X 7，011019（2017）]，我们能够证明对于一般的非平衡稳态系统，平均总熵产生仅受总熵产生上确界的限制，反之亦然。
The expressions for entropy production, free energy, and entropy extraction rates are derived for a Brownian particle that walks in an underdamped medium. Our analysis indicates that as long as the system is driven out of equilibrium, it constantly produces entropy at the same time it extracts entropy out of the system. At steady state, the rate of entropy production ${\dot e}_{p}$ balances the rate of entropy extraction ${\dot h}_{d}$. At equilibrium both entropy production and extraction rates become zero. The entropy production and entropy extraction rates are also sensitive to time. As tim…
In this work, we investigate the relation between the concept of ``information rate'', an information geometric method for measuring the speed of the time evolution of the statistical states of a stochastic process, and stochastic thermodynamics quantities like entropy rate and entropy production. Then, we propose the application of entropy rate and entropy production to different practical applications such as abrupt event detection, correlation analysis, and control engineering. Specifically, by utilising the Fokker-Planck equation of multi-variable linear stochastic processes described by L…
We propose to construct Markov dynamics with specified characteristics using a cycle decomposition of the space of Markov chains introduced by Cohen and Alpern. As an application of this approach, we derive the minimal entropy production required to generate prescribed thermodynamic currents.
Temporal extensivity of Tsallis' entropy and the bound on entropy production rate
Tsallis熵是Boltzmann-Gibbs熵的推广，在复杂系统的非广延统计力学中起着核心作用。近年来，人们在建立Tsallis熵的动力学基础方面做了大量的工作。它们主要研究处于混沌边缘的非线性动力系统。在这里，它是通过推广的热统计公式的基础上的时间平均最近提出的Carati [A。Carati，Physica A 348，110（2005）]，只要相关，由$q$索引的Tsallis熵在时间上是广泛的：时间上的线性增长，即，有限熵产生率然后，熵产生率上的普遍界被证明是$1/|1-q|$。相关概率过程的属性，即，分析了在相空间中决定运动随机性的逗留时间分布。
We study a relationship between optimal transport theory and stochastic thermodynamics for the Fokker-Planck equation. We show that the lower bound on the entropy production is the action measured by the path length of the $L^2$-Wasserstein distance. Because the $L^2$-Wasserstein distance is a geometric measure of optimal transport theory, our result implies a geometric interpretation of the entropy production. Based on this interpretation, we obtain a thermodynamic trade-off relation between transition time and the entropy production. This thermodynamic trade-off relation is regarded as a the…
With nontrivial entropy production, first passage process is one of the most common nonequilibrium process in stochastic thermodynamics. Using one dimensional birth and death precess as a model framework, approximated expressions of mean first passage time (FPT), mean total number of jumps (TNJ), and their coefficients of variation (CV), are obtained for the case far from equilibrium. Consequently, uncertainty relations for FPT and TNJ are presented. Generally, mean FPT decreases exponentially with entropy production, while mean TNJ decreases exponentially first and then tends to a starting si…
