Biological Order as a Consequence of Randomness: Anti-entropy and Symmetry Changes

Abstract

In this chapter, we introduce the notion and the analysis of phenotypic complexity, as anti-entropy, proposed in [Bailly & Longo, 2009] and develop further theoretical consequences. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in evolution and in ontogenesis. Our approach, in particular, will focus on the role of global entropy production and will provide a tool for a mathematical understanding of some fundamental observations by S.J. Gould on how phenotypic complexity increases, on average, along random evolutionary paths, without a bias towards an increase. We also propose a preliminary analysis of biological regenerative processes, which allows to associate entropy production of adults to anti-entropy, by considering “collisions” between entropy and anti-entropy. Lastly, we analyze the situation in terms of theoretical symmetries, in order to further specify the biological meaning of anti-entropy as well as its strong correlations to randomness.