Quantifying entropy production in various active matter phases would open new avenues for probing self-organization principles in these far-from-equilibrium systems. It has been hypothesized that the dissipation of free energy by active matter systems may be optimized to produce highly dissipative dynamical states, hence, leading to spontaneous emergence of more ordered states. This interesting idea has not been widely tested. In particular, it is not clear whether emergent states of actomyosin networks, which represent one of the most salient examples of biological active matter, self-organize following the principle of dissipa- tion optimization. In order to start addressing this question using detailed computational modeling, we rely on the MEDYAN simulation platform, which allows simulating active matter networks from fundamental molecular principles. We have extended the capabilities of MEDYAN to allow quantification of the rates of dissipation resulting from chemical re- actions and relaxation of mechanical stresses during simulation trajectories. This is done by computing precise changes in Gibbs free energy accompanying chemical reactions using a novel formula, and through detailed calculations of instantaneous values of the system’s mechanical energy. We validate our approach with a mean-field model that estimates the rates of dissipation from filament treadmilling. Applying this methodology to the self- organization of small disordered actomyosin networks, we find that compact and highly cross-linked networks tend to allow more efficient transduction of chemical free energy into mechanical energy. In these simple systems, we do not observe that spontaneous network reorganizations lead to increases in the total dissipation rate as predicted by the dissipation- driven adaptation hypothesis mentioned above. However, whether such a principle operates in more general, more complex cytoskeletal networks remains to be investigated.