Quasi-Equilibrium States and Phase Transitions in Biological Evolution.

We developed a macroscopic description of the evolutionary dynamics by following the temporal dynamics of the total Shannon entropy of sequences, denoted by , and the average Hamming distance between them, denoted by . We argue that a biological system can persist in the so-called quasi-equilibrium state for an extended period, characterized by strong correlations between and , before undergoing a phase transition to another quasi-equilibrium state. To demonstrate the results, we conducted a statistical analysis of SARS-CoV-2 data from the United Kingdom during the period between March 2020 and December 2023. From a purely theoretical perspective, this allowed us to systematically study various types of phase transitions described by a discontinuous change in the thermodynamic parameters. From a more-practical point of view, the analysis can be used, for example, as an early warning system for pandemics.