Related papers: Emergence of order in selection-mutation dynamics
Organisms and algorithms learn probability distributions from previous observations, either over evolutionary time or on the fly. In the absence of regularities, estimating the underlying distribution from data would require observing each…
The dynamics of molecular collisions in a macroscopic body are encoded by the parameter Thermodynamic entropy - a statistical measure of the number of molecular configurations that correspond to a given macrostate. Directionality in the…
The evolution of entropy is derived with respect to dynamical systems. For a stochastic system, its relative entropy $D$ evolves in accordance with the second law of thermodynamics; its absolute entropy $H$ may also be so, provided that the…
We analyse the unreduced, nonperturbative dynamics of an arbitrary many-body interaction process with the help of the generalised effective potential method and reveal the well-specified universal origin of change (emergence), time and…
We argue that in Universes where future and past differ only by the entropy content a psychological arrow of time pointing in the direction of entropy increase can arise from natural selection in biological evolution. We show that this…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
We give a closed form of the discrete-time evolution of a recombination transformation in population genetics. This decomposition allows to define a Markov chain in a natural way. We describe the geometric decay rate to the limit…
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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…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…
We define a new variant of exclusion processes in discrete time that has jump probabilities that depend on the last jump performed. In a particular limit for the jump probabilities and in suitable scaling limits for space and time, we…
The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased"…
Understanding the evolution of entropy in the universe is a fundamental aspect of cosmology. This paper investigates the evolution of entropy in a spatially flat $K=0$ universe, focusing on the contributions of matter, radiation, and dark…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
Evolution of the reduced density matrix for a subsystem is studied to determine deviations from its Markov character for a system consisting of a closed chain of $N$ oscillators with one of them serving as a subsystem. The dependence on $N$…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
Evolutionary processes proved very useful for solving optimization problems. In this work, we build a formalization of the notion of cooperation and competition of multiple systems working toward a common optimization goal of the population…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…