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§1.引言 本文讨论由算子Ω= (c_(ij)(x))生成的相空间为E=R~1×Z的马氏过程,其中且系数满足下列条件: 相似文献
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§1 引言在非平衡态统计物理中,统计不可逆性与熵产生率是两个十分重要的概念.在[1]、[2]、[3]中,我们讨论了可以用马氏链描写的系统的可逆性与熵产生率,并证明一个平稳马氏链可逆的充分必要条件是熵产生率为零,进而又说明熵产生率是系统对时间的统计不可逆程度的一个刻划指标.但是,由于马氏链的状态空间的局限性,上述结果不能适应大量连续状态空间的物理问题研究的需要.为此,本文设法对一般的随机过程给出熵产生率的概率定义,并进而 相似文献
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In this paper, we consider that how much information the large deviation rate functions contain. Namely, let us observe two processes Ⅹ~(1) and Ⅹ~(2) with the same large deviation function Ⅰ(μ), for all μ with compact support, and ask what the relation should have between Ⅹ~(1) and Ⅹ(~). In [1], Donsker and Varadhan gave the answer for the case of diffusion as the following theorem. 相似文献
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The problem of metastability has attracted a great attention in the recent decade.In particular, it has been extensively investigated the 2-dimensional Ising model ina finite torus [CFQ]、[NS]、[Sch]. In this paper, the 3-dimensional Ising model withGlauber dynamics under a positive magnetic field is considered. We characterize themetastable behavior in the pathwise approacb, find out all metastable states, anddetermine naturally the critical droplet. We give a general and clear view of the sub-stance of the passage from all spins down (- 1) to all spins up (+ 1). For a largeclass of initial states, the logarithmic asymptotics of the hitting time of - 1 or + 1 areaccurately estimated, and the shrink and growth of droplets are described. 相似文献