Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation

TL;DR

This paper presents an exactly solvable 1D model demonstrating microscopic phase transitions and temperature oscillations in the microcanonical ensemble, revealing insights into evaporation and dissociation processes.

Contribution

It introduces a solvable 1D Lennard-Jones type model showing microscopic phase transitions and temperature oscillations, linking theoretical predictions with experimental evaporation phenomena.

Findings

Microcanonical ensemble exhibits (N-1) non-analytic phase transitions.

Temperature oscillations indicate cooling by evaporation in isolated systems.

Canonical heat capacity shows peaks related to chain dissociation.

Abstract

We calculate exactly both the microcanonical and canonical thermodynamic functions (TDFs) for a one-dimensional model system with piecewise constant Lennard-Jones type pair interactions. In the case of an isolated $N$-particle system, the microcanonical TDFs exhibit (N-1) singular (non-analytic) microscopic phase transitions of the formal order N/2, separating N energetically different evaporation (dissociation) states. In a suitably designed evaporation experiment, these types of phase transitions should manifest themselves in the form of pressure and temperature oscillations, indicating cooling by evaporation. In the presence of a heat bath (thermostat), such oscillations are absent, but the canonical heat capacity shows a characteristic peak, indicating the temperature-induced dissociation of the one-dimensional chain. The distribution of complex zeros (DOZ) of the canonical partition may be used to identify different degrees of dissociation in the canonical ensemble.