Note:Duality of Stochastic Hamiltonian Systems

时间可反演性是确定性哈密顿系统的一个重要性质．由此导出的一个结果就是哈密顿系统的对偶性质，一般情况下，随机哈密顿系统并不具有时间可反演性．一个有趣的问题是：它是否仍然保持了对偶性质？

It is well known that,a Hamiltonian system is time inversable. With this important property one can construct its dual Hamiltonian system. In the stochastic (non deterministic) situation the time inversable property holds no longer true. An interesting question is:if its dual stochastic Hamiltonian system still can be found? This note answers this question.