Related papers: A statistical-mechanical study of evolution of rob…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
We consider an infinite locally finite system (configuration) $\gamma$ of particles distributed over a Euclidean space $X$. Each particle located at $x\in X$ carries an internal parameter (mark, or ``spin'') $\sigma_{x}\in S=\mathbb{R}.$…
Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics.…
The evolution of various competing cell types in tissues, and the resulting persistent tissue population, is studied numerically and analytically in a particle-based model of active tissues. Mutations change the properties of cells in…
The dynamics of a simple spin chain (2 spins) coupled to bosonic baths at different temperatures is studied. The analytical solution for the reduced density matrix of the system is found. The dynamics and temperature dependence of spin-spin…
The relaxation dynamics of many disordered systems, such as structural glasses, proteins, granular materials or spin glasses, is not completely frozen even at very low temperatures. This residual motion leads to a change of the properties…
The microscopic dependence of glassy equilibration on sample history, both the initial configuration and the specific sequence of random noise, is examined. The temporal evolution of spin configurations in a two-dimensional Ising spin glass…
Two dimensional magnetic films with perpendicular magnetization spontaneously form magnetic domain patterns that evolve or undergo symmetry transformations as a function of temperature. When the system is driven from equilibrium by a rapid…
Finite time convergence to functionally important target states is a key component of many biological processes. We previously found that the terminal approach phase of such dynamics exhibits universal types of stochastic dynamics that…
Homophily and social influence are the fundamental mechanisms that drive the evolution of attitudes, beliefs and behaviour within social groups. Homophily relates the similarity between pairs of individuals' attitudinal states to their…
The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an…
This paper deals with the stochastic Ising model with a temperature shrinking to zero as time goes to infinity. A generalization of the Glauber dynamics is considered, on the basis of the existence of simultaneous flips of some spins. Such…
Geographic ranges of communities of species evolve in response to environmental, ecological, and evolutionary forces. Understanding the effects of these forces on species' range dynamics is a major goal of spatial ecology. Previous…
A paradigm for isothermal, mechanical rectification of stochastic fluctuations is introduced in this paper. The central idea is to transform energy injected by random perturbations into rigid-body rotational kinetic energy. The prototype…
Which factors govern the evolution of mutation rates and emergence of species? Here, we address this question using a first principles model of life where population dynamics of asexual organisms is coupled to molecular properties and…
Competing interactions, non-trivial electronic band topology, quantum fluctuations, and the interplay between emergent degrees of freedom in frustrated quantum materials can give rise to a wide range of exotic phenomena. Glassy dynamics,…
We analyze a nonlocal PDE model describing the dynamics of adaptation of a phenotypically structured population, under the effects of mutation and selection, in a changing environment. Previous studies have analyzed the large-time behavior…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
We investigate numerically the dynamics of three different spin models in the aging regime. Each of these models is meant to be representative of a distinct class of aging behavior: coarsening systems, discontinuous spin glasses, and…
Non-equilibrium dynamics of many-body systems is important in many branches of science, such as condensed matter, quantum chemistry, and ultracold atoms. Here we report the experimental observation of a phase transition of the quantum…