Are there phase transitions in evolving systems? If so, what are the “thermodynamic variables” for which the phase transition is observed? How may the phase transitions be characterized, e.g. with critical exponents?
The term phase transition generally refers to changes in the basic state of matter in a physical system, e.g. changes between the basic states of solid, liquid, gas, and plasma, as temperature is varied.
Identification of a phase transition usually requires the identification of a macroscopic physical observable (density, correlation, etc) taken as an average over microscopic degrees of freedom. In the theory of phase transitions, these physical observables are typically derived from the system’s thermodynamic free energy, and may undergo discontinuities as other system variables are varied (e.g. temperature).
The discontinuities observed variables are typically characterized by power laws of the observed variables through the phase transition; e.g. the heat capacity C near the critical temperature T_c goes as
C = |T_c - T|^{-\alpha}
The exponents that characterize these transitions are called critical exponents, and are very interesting because they can be the same across broad classes of systems that have common features in their free energy.
For the study of phase transitions in evolutionary models, there are several issues to be resolved.
- What is the analog of thermodynamic free energy for the model? In the classical statistical mechanics setting, the free energy is usually cast as the log of a partition function, which is formed by counting of microstates. How are microstates characterized for an evolutionary model, and how may they be counted to form a partition function to get a free energy?
- Once a free energy has been defined, how are the relevant observables related to it?
- Can phase transitions be observed, and critical exponents measured, even in the absence of a theoretical understanding of how the thermodynamic free energy is defined?
- Is the classical statistical mechanical paradigm adequate to characterize living states of matter? If not, how need it change?
Topics in this category should generally contain examples of observed phase transition, with reference to the model, including code to reproduce the results and explore further. The observed phase transition should clearly show discontinuous behavior as a temperature-like parameter is varied, ideally with measurement of critical exponents through the transition. Articles already written that report on phase transitions in evolutionary models are fair game, and a good place to start.
The project is focused on measurements characterizing phase transitions in model systems. Purely theoretical considerations should not be included here unless they are grounded with reference to particular model systems and measurements.
This project may overlap with the bifurcation project.