Copyright © 2012 Hitomi Kitaojima and Shigeru Kanemitsu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Aging as the process in which the built-in entropy decreasing function worsens as internal time passes. Thus comes our definition, “life is a one way flow along the intrinsic time axis toward the ultimate heat death, of denumerably many metabolic reactions, each at local equilibrium in view of homeostasis”. However, our disposition is not of reductionismic as have been most of approaches, but it is to the effect that such a complicated dynamic system as lives are not feasible for modelling or reducing to minor fragments, but rather belongs to the whole-ism. Here mathematics can play some essential role because of its freedom from practical and immediate phenomena under its own nose. This paper is an outcome of hard trial of mathematizing scientific disciplines which would allow description of life in terms of traditional means of mathematica, physics. chemistry, biology etc. In the paper, we shall give three basic math-phys-chem approaches to life phenomena, entropy, molecular orbital method and formal language theory, all at molecular levels. They correspond to three mathematical dsciplines—probability, linear algebra and free groups, respectively. We shall give some basics for the Rényi ()-entropy, Chebyshev polynomials and the notion of free groups inrespective places. Toward the end of the paper, we give some of our speculations on life and entropy increase principle therein. Molecular level would be a good starting point for constructing plausible math-phys-chem models.