Energy dissipation of future integrated systems, consisting of a myriad of devices, is a challenge that cannot be solved solely by emerging technologies and process improvements. Even though approaches like Field-Coupled Nanocomputing allow computations near the fundamental energy limits, there is a demand for strategies that enable the recycling of bits' energy to avoid thermalization of information. In this direction, we propose a new kind of partially reversible systems by exploiting fan-outs in logic networks. We have also introduced a computationally efficient method to evaluate the gain obtained by our strategy. Simulation results for state-of-the-art benchmarks indicate an average reduction of the fundamental energy limit by 17% without affecting the delay. If delay is not the main concern, the average reduction reaches even 51%. To the best of our knowledge, this work presents the first post-synthesis strategy to reduce fundamental energy limits for Field-Coupled Nanocomputing circuits.