内时间算子表象中的微观熵和粗粒熵

A STUDY ON THE COARSING GRAIN ENTROPY AND THE MICROSCOPIC ENTROPY IN THE REPRESENTATION OF AN INNER TIME OPERATOR

一、前言从微观角度来描述宏观不可逆性的问题引起了统计物理工作者的极大兴趣。长期以来存在一种普遍的观点:为了得到不可逆的马尔可夫型的动力学方程,需要完成两个步骤。首先要进行某种形式的平均即投影,或曰粗粒化等,把力学方程约化为一个广义的主方程。通常这种方程是非马尔可犬的,它包含着对初始条件的记忆。然后根据物理条件进行适当近似,把广义主方程转变为明显表示出不可逆性的马尔可夫型主方程。对这种演化方程我们可以构造出 Lyapounov 型的函数,例如熵。从刘维方程导出玻尔兹曼方程,

In the representation of an inner time operator T in the Shrdinger's picture the coarsing grain entropy and the so-called microscopic entropy were compared.It is shown that the latter varies monotonously in all conditions while the former depends on the initial preparation of the state.Inversing velocities,the essentially different behaviours of those two entities are shown.The Baker's transformation is used as a simple model to verify the argument.