Mechanism of irreversibility in a many-body systems

TL;DR

This paper proposes a mechanism for irreversibility in many-body systems based on an extended Hamiltonian formalism, linking thermodynamics and classical mechanics through entropy expressed via subsystem interactions.

Contribution

It introduces a generalized Hamiltonian framework for open systems, establishing a connection between thermodynamics and classical mechanics, and deriving a formula for entropy based on subsystem interactions.

Findings

Derived a formula expressing entropy through subsystem interaction forces.

Established a fundamental link between thermodynamics and classical mechanics.

Proposed a mechanism explaining irreversibility in many-body systems.

Abstract

The mechanism of irreversible dynamics in the mixing systems is constructed in the frames of the classical mechanics laws. The offered mechanism can be found only within the framework of the generalized Hamilton's formalism. The generalized formalism is created by expansion of the canonical Hamilton's formalism to the open systems. A formula, which expresses the entropy through the work of subsystems interaction forces was obtained. The essential link between thermodynamics and classical mechanics was established.