Thermodynamics of Markov Systems: Dissipation, Conservation, and Phase Transition
Monday, May 13, 2013 - 2:00pm - 2:50pm
Individual-based population dynamics articulates stochastic behavior of individuals and considers deterministic equations at the population level as an emergent phenomenon. Using chemical species inside a small aqueous volume (a cell) as an example, we introduce Delbrück-Gillespie birth-and-death process for chemical reactions dynamics. Using this formalism, we (1) illustrate the relation between nonlinear saddle-node bifurcation and first- and second-order phase transition; (2) introduce a thermodynamic theory for entropy and entropy production and prove 1st and 2nd Laws-like theorems; and (3) show a completely consistency between dynamics and the newly developed thermodynamics. To physics: we discuss the fundamental issue of what is dissipation and its relation to time reversibility in subsystems. To biology: we suggest the inter-basin-of-attraction stochastic dynamics as a possible mechanism for epigenetic variations at the cellular level.