Evolutionary Dynamics, Evolutionary Forces, and Robustness: A Nonequilibrium Statistical Mechanics Perspective

Any realistic evolutionary theory has to consider: (i) the dynamics of organisms that reproduce and possess heritable traits; (ii) the appearance of stochastic variations in these traits; and (iii) the selection of those organisms that better survive and reproduce. These elements shape the “evolutionary forces” that characterize the evolutionary dynamics. Here, we introduce a general model of reproduction–variation–selection dynamics. By treating these dynamics as a non-equilibrium thermodynamic process, we make precise the notion of the forces that characterize evolution. One of these forces, in particular, can be associated with the robustness of reproduction to variations. The emergence of this trait in our model—without any explicit selection for it—is an example of a general phenomenon, which can be called enaptation, distinct from the well-known and studied phenomena of adaptation and exaptation. Some of the detailed predictions of our model can be tested by quantitative laboratory experiments, similar to those performed in the past on evolving populations of proteins or viruses.

Nonequilibrium Entropy Conservation and the Transport Equations of Mass, Momentum, and Energy

Nonequilibrium statistical mechanics or molecular theory has put the transport equations of mass, momentum and energy on a firm or rigorous theoretical foundation that has played a critical role in their use and applications. Here, it is shown that those methods can be extended to nonequilibrium entropy conservation. As already known, the “closure” of the transport equations leads to the theory underlying the phenomenological laws, including Fick’s Law of Diffusion, Newton’s Law of Viscosity, and Fourier’s Law of Heat. In the case of entropy, closure leads to the relationship of entropy flux to heat as well as the Second Law or the necessity of positive entropy generation. It is further demonstrated how the complete set of transport equations, including entropy, can be simplified under physically restrictive assumptions, such as reversible flows and local equilibrium flows. This analysis, in general, yields a complete, rigorous set of transport equations for use in applications. Finally, it is also shown how this basis set of transport equations can be transformed to a new set of nonequilibrium thermodynamic functions, such as the nonequilibrium Gibbs’ transport equation derived here, which may have additional practical utility.

Non-coherent diffusion of a vacancy in a one-dimensional lattice in the quasiclassical approximation

A vacancy in a one-dimensional lattice is considered as a vacant site in a one-dimensional chain of atoms. The energy model of this system is a double potential well with two levels. Based on the relations of nonequilibrium statistical mechanics, including the Kubo formula for the transport coefficient, the frequency of vacancy jumps is calculated. In this case, two factors of the system perturbation are taken into account: lattice deformation associated with the formation of an empty site, and phonon scattering by mass fluctuations in the chain. An analysis of two high-temperature jumps is given. First, the classical limit of vacancy motion under weak coupling conditions is considered for small values of the gradient of the interaction potential of the defect with the chain. In the classical case, the transition of an atom adjacent to a vacancy occurs through a quasy-stationary excited state. Secondly, a jump under tight binding conditions, when the motion of a neighboring atom occurs through a quasistationary state of finite width, and therefore having a finite lifetime.

Hydrodynamic and Thermodynamic Nonequilibrium Effects around Shock Waves: Based on a Discrete Boltzmann Method

A shock wave that is characterized by sharp physical gradients always draws the medium out of equilibrium. In this work, both hydrodynamic and thermodynamic nonequilibrium effects around the shock wave are investigated using a discrete Boltzmann model. Via Chapman–Enskog analysis, the local equilibrium and nonequilibrium velocity distribution functions in one-, two-, and three-dimensional velocity space are recovered across the shock wave. Besides, the absolute and relative deviation degrees are defined in order to describe the departure of the fluid system from the equilibrium state. The local and global nonequilibrium effects, nonorganized energy, and nonorganized energy flux are also investigated. Moreover, the impacts of the relaxation frequency, Mach number, thermal conductivity, viscosity, and the specific heat ratio on the nonequilibrium behaviours around shock waves are studied. This work is helpful for a deeper understanding of the fine structures of shock wave and nonequilibrium statistical mechanics.