信息熵通过系统变化规律的研究

Study of variational law of information entropy passing through systems

对孤立热力系统中的不可逆过程，热力系统熵自发不可逆地增加；而对自发进行的物理变化过程，物理场熵是减小的．迄今，信息系统中信息熵的变化规律尚不十分明确．对此进行研究，得出结论：带限平稳正态随机信号通过因果最小相位线性系统后，熵可增加或减小，可用线性逆系统使熵可逆变化；平稳非正态独立同分布随机信号通过因果非最小相位线性系统后，熵恒增加，并趋近平稳正态信号，使熵趋于最大．原线性系统不能使熵可逆变化，亦不存在线性逆系统使熵可逆变化．只有加负熵或等效地通过一非线性系统，才能使熵减至最小．

For irreversible processes in an isolated thermodynamic system,the thermodynamicentropy increases spontaneously and irreversibly,while for spontaneous physical processes,physical field entropy decreases. Up to now,the variational law of information entropy ininformation systems is not quite clear yet.This is studied and the following conclusions aregiven:After a frequency-banded stationary normal random signal passes causal minimum phaselinear systems,its entropy may increase or decrease and linear inverse systems can be used toinversely change entropy.After a stationary non-normal i. i.d.random signal passes causal non-minimum phase linear systems,it tends towards stationary normal signal,while its entropyconstantly increases and tends towards maximum. The primary system cannot inversely changeentropy, nor can any linear inverse system. Only by adding minus entropy,or equivalentlypassing through a nonlinear system can entropy decrease to minimum.