On the objective origin of the phase transitions and metastability in many-particle systems

TL;DR

This paper explores the microscopic origins of phase transitions and metastability in many-particle systems, proposing an enhanced Hamiltonian approach to better connect statistical mechanics with thermodynamics, especially near critical points.

Contribution

It introduces a novel method using a temperature-dependent Hamiltonian to incorporate feedback between microscopic and macroscopic states, improving the description of phase transitions.

Findings

The approach models metastable states in finite systems.

Application to a water-like medium illustrates practical relevance.

Enhanced Hamiltonian captures phase transition phenomena more accurately.

Abstract

Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to description of the macroscopic properties of real condensed media within wide thermodynamic ranges, including the vicinities of the phase transition points. A particular problem is the absence of metastable states in the Gibbs statistical mechanics of the systems composed of finite number of particles. Nevertheless, accordance between equilibrium statistical mechanics and thermodynamics of condensed media is achievable if to take account of the mutual correlation (the feedback) between the microscopic properties of molecules and the macrostate of the corresponding medium. This can be done via usage of the "enhanced" Hamilton operator of the considered many-particle system, which contains some temperature-dependent term(s), and the following introduction of the generalized equilibrium distribution over microstates. For illustration of the reasonableness of the proposed approach (and of its availability in practical applications), a cell model of melting/crystallization and metastable supercooled liquid for a water-like medium is presented.