 Entropic network modulus

A network of flexible thermally fluctuating strands stores an order-$k_{B}T$ elastic free-energy change per active strand under an order-one deformation. For active-strand number density $n$, its shear modulus is therefore of order $n{k}_{B}T$. If one active element occupies a mesh volume $m^3$, this becomes $k_{B}T/m^3$. The numerical coefficient depends on network connectivity, defects and the deformation model. A mesh size alone does not fix the modulus of a general athermal or bending-dominated network; strand stiffness is then additional input.