Dissipative systems entropy

TL;DR

This paper introduces an infinite-dimensional phase space for dissipative systems, demonstrating that in this space entropy remains constant and that dissipation arises when transitioning to finite-dimensional phase spaces.

Contribution

It presents a novel framework using infinite-dimensional phase space to analyze dissipative systems, showing entropy invariance in this space and explaining dissipation as a consequence of dimensional reduction.

Findings

In infinite-dimensional phase space, entropy is constant.

Transition to finite-dimensional space causes entropy change and dissipation.

Dissipative systems can be viewed as conservative in an extended phase space.

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.