## as a nonequilibrium statistical physics problem – SIR model

In Results, we use a slightly different formulation of the problem, in which two different temperatures, *T _{V}* and

*T*, were assigned to the volume and length dimensions of dendritic spines. Subsequently, instead of maximizing the Lagrange function of , we minimize the grand potential of synaptic connectivity (): Such two-temperature formulation is used to describe quasi-equilibria in some statistical physics problems (; ), in which different components of the systems are not in equilibrium with each other but are in quasi-equilibria on their own. Results shown in ,

_{s}*E*and

*F*, and

*A*suggest that this may be the case in the developing cerebral cortex. Quasi-equilibrium state may result from synaptic strength and structural synaptic plasticity mechanisms having separate energy budgets or because the equilibration timescales of the two plasticity mechanisms are much shorter than the overall equilibration time (i.e., the time it takes to reach adulthood). Needless to say, the optimization problems of and become identical in statistical equilibrium where

*T*=

_{V}*T*=

_{s}*T*.

A detailed discussion illustrating the potential of the stochastic representation in statistical physics problems. The use of polynomial functionals of the white noise process is shown for the treatment of certain nonlinear random processes. It is ...