Time, Entropy and Structuredness in Biological Systems and Their Dynamics in the Process of Development and Evolution

Abstract

Evolution in modern science is one of the clear manifestations of the one-pointedness of time and its direction. As we showed earlier, algorithmic complexity, like Shannon's information and Boltzmann's entropy, tends to increase per the general law of complication. This tendency determines this direction of time and evolution. However, the algorithmic complexity of most material systems does not reach its maximum, that is, a chaotic state, due to this or that law of nature that create various structures. The complexity of such structures is very different from the algorithmic complexity, and I propose a formula for calculating such structural complexity, which I called structuredness. The structure of any material system depends on the structures of three main types: stable, dissipative, and post-dissipative. The latter is defined as stable structures created by dissipative, directly or indirectly. The appearance of such structures can lead to the occurrence of "ratchet" processes that determine the structuregenesis in inanimate and, especially, in living systems. The limit of the structuregenesis (maximal structuredness) of a system depends on its entropy capacity. For simple systems, this capacity, equal to the maximum entropy, is determined only by the size of the system (the number of its elements). In the more complex cases, however, the entropy capacity may also depend on the number of types of elements, the number of levels of its structural hierarchy, and the thickness of the temporal structure of the system. The temporal structure of biological systems, especially those highly organized, such as eukaryotes and multicellular organisms, is quite complex and even 2-dimensional. This 2-dimensionality of biological time adds another dimension to entropy capacity. Representation of biological time by complex numbers allows us to combine the exponential growth of organisms and their periodic physiological processes with the same dynamic equation. Finally, I consider the specific dynamics of the internal entropy of living organisms in a complex time.