Entropy production in stochastic Riemannian geometries with applications to chemical ecology

AbstractDiffusion theories obtained from the geodesic equations of a Riemannian metric on Rn are considered. A theorem on the rate of production of entropy for a class of such theories is proved, showing that this rate depends on a certain curvature related invariant, whose sign influences this rate. Also considered are stationary densities for a class of conformally flat metrics whose volume density is Gaussian. The entropy of such densities is shown to be a function of a temperature-like parameter. These results are interpreted in the context of chemical ecology via Volterra-Hamilton systems and Antonelli's concept of vigour