Phase transitions and phase coexistence: equilibrium systems versus externally driven or active systems - Some perspectives

ABSTRACT

A tutorial introduction to the statistical mechanics of phase transitions and phase coexistence is presented, starting out from equilibrium systems and nonequilibrium steady-state situations in externally driven systems, such as unmixing of sheared binary fluid mixtures, the driven lattice gas model, and the onset of Rayleigh-Bénard convection. Then, some models for phase separation in models for active systems, where particles possess internal motility, are discussed, emphasizing what one can learn by extending analysis methods to study phase transitions in equilibrium systems by computer simulations to active systems. Specific examples will include colloid-polymer mixtures where the colloids are assumed to be active particles, and active Brownian particles. The extent to which concepts familiar from the study of equilibrium systems are still useful will be critically discussed.

KEYWORDS:

• Active Brownian Particles
• critical exponents
• finite size scaling
• Asakura-Oosawa model

Acknowledgments

The authors had the privilege of a stimulating collaboration with S. K. Das, F. Dittrich, S. A. Egorov, F. Schmid, J. T. Siebert, T. Speck and B. Trefz in some preceding original work [10, 12, 16]. It is a pleasure to thank them for many insightful discussions, and for permitting them to reproduce some figures. PV gratefully acknowledges the financial support by the Deutsche Forschungsgemeinschaft within priority program SPP 1726 (Grant VI 237/5-2). The authors gratefully acknowledge the computing time granted on the supercomputer Mogon at Johannes Gutenberg University Mainz (hpc.uni-mainz.de).

Additional information

Funding

This work was supported by the Deutsche Forschungsgemeinschaft [VI 237/5-2].