Dissipative systems entropy

Abstract

In this paper, we introduce the generalized phase space $\left(\vec{r},\vec{v},\dot{\vec{v}},\ddot{\vec{v}},...\right)$, which expands the known phase space $\left(\vec{r},\vec{v}\right)$. The fact is that the introduced space is the infinity dimensional phase space. The paper shows that dissipative systems in generalized phase space may be considered as conservative systems. It is shown that, in infinity dimensional phase space, the entropy is a constant value. It is shown that the transition to finite dimensional phase space leads to dissipations and change of the entropy. The paper contains the rigorous mathematical result.

23 pages, 3 figures