Linear Surprisal and Simple Birth, Death and Immigration Process : Condensed Matter and Statistical Physics

概要

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In the conservative Hamiltonian systems, once a distribution of maximal entropy (subject to constraints) is achieved, the exact solution of the Liouville equation is one of the maximal entropy (subject to other constraint conditions), at any moment after that. This is stated in terms of surprisal analysis (a constrained statistical analysis motivated by information-theoretical considerations) as follows: If once the surprisal of a state happens to be linear as a function of measured dynamical variables, it remains linear as a function of the set of dynamical variables which are coupled to the initially measured ones. Taking advantage of this (the preservation of linear surprisal) an investigation is made to incorporate the idea of maximal entropy procedure in the framework of stochastic process. The subject of consideration was limited to the class of "general birth and death process". Among the family of stochastic processes belonging to this class the "simple birth, death and immigration process" was found to fulfill the necessary and sufficient conditions for the preservation of linear surprisal, so that to be appropriate in describing the states of maximal entropy governed by the Liouville equation.
理論物理学刊行会の論文
1987-02-25