The Liouville equation in infinitely dimensional separable Hilbert space (Q1073586)

The Liouville equation is derived in the case when the phase space of a system with an infinite countable number of degrees of freedom is an infinitely dimensional separable Hilbert space. For such systems it is possible to define the counterparts of the basic concepts of mechanics with a finite number of degrees of freedom. In this work, use is made of the counterpart of the notion of divergence. The almost-invariant measure was assumed as the initial state of the system with an infinite countable number of degrees of freedom. The obtained Liouville equation contains an additional term dependent also on the assumed initial state which vanished when we pass to a system with a finite number of degrees of freedom but which is not equal to zero when we consider a system with an infinite countable number of degrees of freedom.