Evolutionary dynamics, evolutionary forces, and robustness: A nonequilibrium statistical mechanics perspective

Evolutionary Implications of Environmental Toxicant Exposure

Homo sapiens have been exposed to various toxins and harmful compounds that change according to various phases of human evolution. Population genetics studies showed that such exposures lead to adaptive genetic changes; while observing present exposures to different toxicants, the first molecular mechanism that confers plasticity is epigenetic remodeling and, in particular, DNA methylation variation, a molecular mechanism proposed for medium-term adaptation. A large amount of scientific literature from clinical and medical studies revealed the high impact of such exposure on human biology; thus, in this review, we examine and infer the impact that different environmental toxicants may have in shaping human evolution. We first describe how environmental toxicants shape natural human variation in terms of genetic and epigenetic diversity, and then we describe how DNA methylation may influence mutation rate and, thus, genetic variability. We describe the impact of these substances on biological fitness in terms of reproduction and survival, and in conclusion, we focus on their effect on brain evolution and physiology.

Emergent second law for non-equilibrium steady states

The Gibbs distribution universally characterizes states of thermal equilibrium. In order to extend the Gibbs distribution to non-equilibrium steady states, one must relate the self-information \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{\mathcal{I}}}}}}}}(x)=-\!\log ({P}_{{{{{{{{\rm{ss}}}}}}}}}(x))$$\end{document}I(x)=−log(Pss(x)) of microstate x to measurable physical quantities. This is a central problem in non-equilibrium statistical physics. By considering open systems described by stochastic dynamics which become deterministic in the macroscopic limit, we show that changes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\Delta }}{{{{{{{\mathcal{I}}}}}}}}={{{{{{{\mathcal{I}}}}}}}}({x}_{t})-{{{{{{{\mathcal{I}}}}}}}}({x}_{0})$$\end{document}ΔI=I(xt)−I(x0) in steady state self-information along deterministic trajectories can be bounded by the macroscopic entropy production Σ. This bound takes the form of an emergent second law \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\Sigma }}+{k}_{b}{{\Delta }}{{{{{{{\mathcal{I}}}}}}}}\,\ge \,0$$\end{document}Σ+kbΔI≥0, which contains the usual second law Σ ≥ 0 as a corollary, and is saturated in the linear regime close to equilibrium. We thus obtain a tighter version of the second law of thermodynamics that provides a link between the deterministic relaxation of a system and the non-equilibrium fluctuations at steady state. In addition to its fundamental value, our result leads to novel methods for computing non-equilibrium distributions, providing a deterministic alternative to Gillespie simulations or spectral methods.

Contrary to states of thermal equilibrium, there is no universal characterization of non-equilibrium steady states displaying constant flows of energy and/or matter. Here, the authors make progress in this direction by deriving an emergent and stricter version of the second law of thermodynamics.