Energy-Directed, Probabilistic, Self-Assembly

The Universe and Life arose through a process of energy-directed, probabilistic self-assembly, or Abiogenesis. Our surrounding macroscopic world of Living Systems appears to be deterministic and yet is governed purely by chance at the elementary particle, nuclear, atomic, and molecular level. In this chapter we provide an understanding of the probabilistic underpinnings of Life. Probability is defined in both its inclusive and exclusive guises. The important means and dispersions of probability distributions are derived and defined. The discrete random walk is used as the basis for understanding interesting biological problems, including diffusion and the structure of random-coil polymers. The large number limit of the binomial distribution is shown to produce the Gaussian distribution. Further extensions lead to the important exponential, Poisson, Fermi–Dirac, Bose–Einstein, and Maxwell–Boltzmann probability distributions. The Fermi–Dirac distribution is the raison d’etre of Life.