Extremum properties of entropy to determine dynamics of growth and evolution in complex systems

An extremum principle is formulated for the q-entropy in evolving biological systems with variable number of states. Evolution for animals with multiple organs is considered. A variational problem is that of maximum entropy subject to the geometric constraint of the constant thermodynamic distance in the (generally non-Euclidean) space of independent probabilities pi plus possibly other constraints. Tensor form of associated dynamics is obtained. Some developmental processes are shown to progress in a relatively undisturbed way, whereas others may terminate in a rapid way due to inherent instabilities.