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 Delbruck-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; (3) show how an analytical mechanics (i.e., Lagrangian and Hamilton-Jacobi systems) arises and the meaning of kinetic energy.  To biology: we suggest the inter-attractoral stochastic dynamics as a possible mechanism for epigenetic variations at the cellular level. To physics: we discuss the fundamental issue of "what is dissipation" and its relation to time reversibility in subsystems.