Quasi-equilibrium states and phase transitions in biological evolution

TL;DR

This paper introduces a macroscopic framework for understanding biological evolution through entropy and Hamming distance, revealing quasi-equilibrium states and phase transitions, with applications to pandemic monitoring.

Contribution

It develops a novel macroscopic description of evolutionary dynamics using entropy and Hamming distance, and demonstrates its application to SARS-CoV-2 data for early pandemic detection.

Findings

Identification of quasi-equilibrium states in evolution

Detection of phase transitions in viral evolution

Potential use as early warning system for pandemics

Abstract

We develop a macroscopic description of the evolutionary dynamics by following the temporal dynamics of the total Shannon entropy of sequences, denoted by $S$, and the average Hamming distance between them, denoted by $H$. We argue that a biological system can persist in the so-called quasi-equilibrium state for an extended period, characterized by strong correlations between $S$ and $H$, 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 allows 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.