Microcanonical phase transitions in small systems

TL;DR

This paper investigates microcanonical phase transitions in small systems, revealing entropy discontinuities and negative specific heat regions associated with broken ergodicity, demonstrated through a simple Lennard-Jones chain model.

Contribution

It introduces the analysis of microcanonical phase transitions in small systems using volume entropy and illustrates phenomena like entropy jumps and negative specific heat.

Findings

Discontinuous jumps in entropy at critical energies

Presence of convex intruders in entropy function

Negative specific heat regions in small systems

Abstract

When studying the thermodynamic properties of mesoscopic systems the most appropriate microcanonical entropy is the volume entropy, i.e. the logarithm of the volume of phase space enclosed by the hypersurface of constant energy. For systems with broken ergodicity, the volume entropy has discontinuous jumps at values of energy that correspond to separatrix trajectories. Simultaneously there is a convex intruder in the entropy function and a region of negative specific heat below such critical energies. We illustrate this with a simple model composed of a chain of 3 particles which interact via a Lennard-Jones potential.