Microcanonical vs. canonical thermodynamics

TL;DR

This paper compares microcanonical and canonical thermodynamics, showing how phase transitions can be defined for finite systems and demonstrating similarities in transition properties for small particle systems like Na, K, and Fe.

Contribution

It provides a clear framework for defining and classifying first-order phase transitions in finite systems without relying on the thermodynamic limit.

Findings

Microcanonical transition temperature and latent heat are similar to bulk values for 200-3000 particles.

Phase transition properties are consistent across different elements like Na, K, and Fe.

Surface atom number remains constant during transition due to multifragmentation.

Abstract

The microcanonical ensemble is in important physical situations different from the canonical one even in the thermodynamic limit. In contrast to the canonical ensemble it does not suppress spatially inhomogeneous configurations like phase separations. It is shown how phase transitions of first order can be defined and classified unambiguously for finite systems without the use of the thermodynamic limit. It is further shown that in the case of the 10-states Potts model as well for the liquid-gas transition in Na, K, and Fe the microcanonical transition temperature, latent heat and interphase surface tension are similar to their bulk values for $\sim 200-3000$ particles. For Na and K the number of surface atoms keeps approximately constant over most of the transition energies because the evaporation of monomers is compensated by an increasing number of fragments with $\ge 2$ atoms (multifragmentation).