Mechanics of population aging and survival.

In this paper we extend the previous work of Witten and her team on defining a classical physics-driven model of survival in aging populations (Eakin, Bull Math Biol 56(6):1121-1141, 1994; Eakin and Witten, Mech Aging Dev 78(2):85-101, 1995; Witten and Eakin, Exp Gerontol 32(2):259-285, 1997) by revisiting the concept of a force of aging and introducing the concepts of a momentum of aging, a kinetic energy and a potential energy of an aging population. We further extend the analysis beyond the deterministic Newtonian mechanics of a macroscopic population as a whole by considering the probabilistic nature of survival of individual population cohort members, thus producing new statistical physics-based concepts of entropy and of a gerontological "temperature". These new concepts are then illustrated with application to the classic parametric Gompertz survival model, which is a commonly used empirical descriptor for survival dynamics of mammalian species, human populations in particular. As a function of chronological age the Gompertz Model force, momentum, and power are seen to have an asymmetric unimodal peak profile, while the potential energy has a descending sigmoidal profile similar to that of the survival fraction. The "temperature" is an exponential function of age and the entropy for a future age at a current census age can be represented as a topological surface with an asymmetric unimodal hump.