From microscopic dynamics to macroscopic irreversibility

TL;DR

This paper proves that in an isolated N-body system with an equilibrium state, entropy cannot decrease and must be non-negative, extending the von Neumann entropy to reduced density operators and deriving related equilibrium and dissipated energy expressions.

Contribution

It introduces a generalized entropy functional based on n-particle reduced density operators and proves its non-decreasing nature in isolated systems with equilibrium.

Findings

Entropy of an isolated system cannot decrease.

Derived explicit form of equilibrium reduced density operators.

Provided expressions for dissipated energy in irreversible processes.

Abstract

In this contribution we prove that the entropy of an N-body isolated system can not decrease and the entropy production should be non-negative provided the system possesses an equilibrium state. We define the entropy as a functional of the set of n-particle reduced density operators (n=0,....,N) generalizing the von Neumann fine-grained entropy formula. Additionally, as a consequence of our analysis we find the expression of the equilibrium n-particle reduced density operators which enter the definition of the entropy as well as the dissipated energy in an irreversible process.