Free energy in a Markovian model of a lattice spin system
Free energy in a Markovian model of a lattice spin system
复制标题
晶格自旋系统马尔可夫模型中的自由能
DOI：
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发表时间：
1971
期刊：
影响因子：
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通讯作者：
R. Holley
中科院分区：
文献类型：
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作者：
R. Holley
一个马尔可夫过程，它可以被认为是一个经典的晶格自旋系统被认为是。系统的态是位形空间上的概率测度，我们研究了这些态的自由能随时间的演化。证明了对于所有的初态，自由能都是不增的，并且它严格地从任何平移不变但不是平衡态的初态开始减少。最后，我们证明了系统的状态弱收敛到给定的相互作用的吉布斯分布的集合，所有的移动不变的平衡态是吉布斯分布。
A Markov process which may be thought of as a classical lattice spin system is considered. States of the system are probability measures on the configuration space, and we study the evolution of the free energy of these states with time. It is proved that for all initial states the free energy is nonincreasing and that it strictly decreases from any initial state which is shift invariant but not an equilibrium state. Finally we show that the state of the system converges weakly to the set of Gibbsian Distributions for the given interaction, and that all shift invariant equilibrium states are Gibbsian Distributions.