GENERALIZED LAGRANGIAN APPROACH AND BEHAVIOR OF LIVING SYSTEMS

Book excerpt: The Lagrangian approach had, in many respects, yielded significant success of theoretical physics in the centuries following its discovery. Unfortunately, the Lagrangian equations, in its original form, cannot be applied to living systems. For a time-independent Lagrangian, these equations are time-reversible and lead to energy conservation, which undoubtedly is not true for the living objects. In this book we show that natural (although rather unexpected) generalization of the Lagrangian enables directly use the apparatus of Lagrangian dynamics to describe behavior the living objects. It is, ultimately, not a revolutionary modification. Rather, lost opportunity that was not considered in the development of contemporary physics has been revisited. The main difference between living creatures and non-living things is that life actively counteracts its degradation in a continuously changing environment. Attempting to minimize the likelihood of death is a basic feature of living organisms. In this book, we assume that the best candidate for an indicator of proximity to death is stress, which is naturally related to the undesirable states of an organism. It will be shown that such an assumption facilitates the design of the generalized Lagrangians and that exploring even the lowest approximation of the Lagrangians allows for a reasonable description of a wide class of behavior of living beings, ranging from bacterial chemotaxis to homeostasis, dominance a hierarchy formation in the social groups and behavior of living being in environment. Although the book intendent, mainly, for young physicists and mathematicians, whose seek promising areas to apply their professional skills, experienced researchers would find here novel powerful theoretical apparatus for their investigation.