Entropy-Based Modeling and Simulation of Evolution in Biological Systems

Abstract

We report computer-aided modeling and simulation of evolution in biological systems with living organisms as effect of extremum properties of classical statistical entropy of Gibbs-Boltzmann type or its associates, e.g. Tsallis q-entropy. Evolution for animals with multiple organs is considered. A variational problem searches for the maximum entropy subject to the geometric constraint of constant thermodynamic distance in a non-Euclidean space of independent probabilities p _i , plus possibly other constraints. Tensor dynamics is found. Some developmental processes progress in a relatively undisturbed way, whereas others may terminate rapidly due to inherent instabilities. For processes with variable number of states the extremum principle provides quantitative eveluation of biological development. The results show that a discrete gradient dynamics (governed by the entropy) can be predicted from variational principles for shortest paths and suitable transversality conditions.