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Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich history, examination of the time-dependent non-equilibrium dynamics has been less studied. In this paper we first derive a generalized master equation in the genotype space for diploid organisms incorporating the processes of selection, mutation, recombination, and reproduction. The master equation is defined in terms of continuous time and can handle an arbitrary number of gene loci and alleles, and can be defined in terms of an absolute population or probabilities. We examine and analytically solve several prototypical cases which illustrate the interplay of the various processes and discuss the timescales of their evolution. The entropy production during the evolution towards steady state is calculated and we find that it agrees with predictions from non-equilibrium statistical mechanics where it is large when the population distribution evolves towards a more viable genotype. The stability of the non-equilibrium steady state is confirmed using the Glansdorff-Prigogine criterion.
Evolution is the fundamental physical process that gives rise to biological phenomena. Yet it is widely treated as a subset of population genetics, and thus its scope is artificially limited. As a result, the key issues of how rapidly evolution occur
We introduce a discrete-time quantum dynamics on a two-dimensional lattice that describes the evolution of a $1+1$-dimensional spin system. The underlying quantum map is constructed such that the reduced state at each time step is separable. We show
The purpose of this roadmap article is to draw attention to a paradigm shift in our understanding of evolution towards a perspective of ecological-evolutionary feedback, highlighted through two recent highly simplified examples of rapid evolution. Th
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We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, like dengue, and the threshold of the disease. The coexistence space is composed by two structures representing the human and mosquito populatio