Some illustrations of information geometry in biology and physics

Many real processes have stochastic features which seem to be representable in some intuitive sense as `close to Poisson', `nearly random', `nearly uniform' or with binary variables `nearly independent'. Each of those particular reference states, defined by an equation, is unstable in the formal sense, but it is passed through or hovered about by the observed process. Information geometry gives precise meaning for nearness and neighbourhood in a state space of processes, naturally quantifying proximity of a process to a particular state via an information theoretic metric structure on smoothly parametrized families of probability density functions. We illustrate some aspects of the methodology through case studies: inhomogeneous statistical evolutionary rate processes for epidemics, amino acid spacings along protein chains, constrained disordering of crystals, distinguishing nearby signal distributions and testing pseudorandom number generators