Related papers: Time Evolution of Entropy in a Growth model: Depen…
`Entropy' appears as driving force in many different evolution equations, both deterministic and stochastic, and in these equations this `entropy' also takes different forms. We show how all these examples can be understood as different…
We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
In this paper we revisit the concept of mobility entropy. Over time, the structure of spatial interactions among urban centres tends to become more complex and evolves from centralised models to more scattered origin and destination…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
A mechanism is proposed that allows to interpret the temporal evolution of a physical system as a result of the inability of an observer to record its whole state and a simple example is given. It is based on a review of the concepts of…
For any discrete time dynamical system with a rational evolution, we define an entropy, which is a global index of complexity for the evolution map. We analyze its basic properties and its relations to the singularities and the…
We use a simple hard-core gas model to study the dynamics of small exploding systems. The system is initially prepared in a thermalized state in a spherical container and then allowed to expand freely into the vacuum. We follow the…
Configurational entropy is an important factor in the free energy change of many macromolecular recognition and binding processes, and has been intensively studied. Despite great progresses that have been made, the global sampling remains…
We model evolution of plants in a world, made up of different locations, with multiple environments (mutually exclusive and collectively exhaustive subsets of locations). Each environment (landmass) has temperature, rainfall, and other…
The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
We study the growing time scales and length scales associated with dynamical slow down for a realistic glass former, using computer simulations. We perform finite size scaling to evaluate a length scale associated with dynamical…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…
Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…
We investigate the time evolution of the Boltzmann entropy of a dilute gas of N particles, N>>1, as it undergoes a free expansion doubling its volume. The microstate of the system, a point in the 4N dimensional phase space, changes in time…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
The living organism is considered as an open system, whereas Prigogine's approach to the thermodynamics of such systems is used. The approach allows one to formulate the law of individual growth and development (ontogenesis) of the living…
According to the second law of thermodynamics, the arrow of time points to an ever increasing entropy of the Universe. However, exactly how the entropy evolves with time and what drives the growth remain largely unknown. Here, for the first…
We present an individual based model of evolutionary ecology. The reproduction rate of individuals characterized by their genome depends on the composition of the population in genotype space. Ecological features such as the taxonomy and…