<p>Contractile biopolymer networks, such as the actomyosin meshwork of animal cells, are ubiquitous in living organisms. The active gel theory, which provides a thermodynamic framework for these materials, has been mostly used in conjunction with the assumption that the microstructure of the biopolymer network is based on rigid rods. However, experimentally, crosslinked actin networks exhibit entropic elasticity. Here we combine an entropic elasticity kinetic theory, in the spirit of the Green and Tobolsky model of transiently crosslinked networks, with an active flux modelling biological activity. We determine this active flux by applying Onsager reciprocal relations to the corresponding microscopic dynamics. We derive the macroscopic active stress that arises from the resulting dynamics and obtain a closed-form model of the macroscopic mechanical behaviour. We show how this model can be rewritten using the framework of multiplicative deformation gradient decomposition, which is convenient for the resolution of such problems.</p>