The Arruda–Boyce model is based on the statistical mechanics of polymer chains.  In this approach, each macromolecule is described as a chain of  segments, each of length .  If we assume that the initial configuration of a chain can be described by a random walk, then the initial chain length is
If we assume that one end of the chain is at the origin, then the probability that a block of size  around the origin will contain the other end of the chain, , assuming a Gaussian probability density function, is
The configurational entropy of a single chain from Boltzmann statistical mechanics is
where  is a constant.  The total entropy in a network of  chains is therefore
where an affine deformation has been assumed.  Therefore the strain energy of the deformed network is
where  is the temperature.