Energy limits and evolution in biological systems 375 10.3. TOWARD A QUANTITATIVE DESCRIPTION OF DEVELOPMENT AND EVOLUTION OF SPECIES Mechanical views are abandoned when development and evolution of species are described. The results of observations in development and evolution imply that the increase in number of states is governed by gradient of a complexity function based on the information-theoretic entropy. Covariant tensor form of associated dynamics can be obtained. For the accepted model of complexity, some developmental processes may progress in a relatively undisturbed manner, whereas others may terminate in a rapid way due to inherent instabilities. Nowa- days these features can be predicted by describing complex evolutions in terms of principles for shortest paths in their state spaces along with suitable transver- sality conditions. Reversible modification of states constitutes a basic reference frame to describe mutations. With this information, it may be discussed how appropriate and operative for complex-system modeling are diverse measures of complexity, including the information content of the genome or that based on genetic code, which are complexities measured by a molecular biologist. In a number of recent works non-equilibrium thermodynamics is regarded as the basis for an alternative evolutionary hypothesis. Since Darwin (1859), various researchers found ways to describe evolution and various theoretical