Stochastic Applied Mathematics and Biology

There is a growing awareness toward a slow shifting in the foundation of the thermodynamic laws, from several macroscopic, empirical postulates concerning heat as a form of random mechanical motions, to derivable mathematical theorems based on stochastic dynamics of mesoscopic systems. It becomes increasingly clear that a stochastic dynamic description of the Nature is a very effective mathematical representation of the Reality. This is particularly true for the world of biology. In this talk, I shall first introduce mathematical thermodynamics as a set of mathematical results in stochastic processes. The result is then applied to complex biochemical kinetic systems. Via the limit, by merely taking the molecular numbers to be infinite, we can derive J. W. Gibbs' macroscopic isothermal equilibrium chemical thermodynamics and generalize it to mesoscopic nonequilibrium systems such as biological cells.

Event Topic

Stochastic & Multiscale Modeling and Computation