Amid the escalating global focus on renewable energy, Multi-Energy Systems (MES) within distribution networks have emerged as crucial facilitators in addressing diverse energy requirements. This study delves into the collaborative interplay among energy sources, storage, and load within these networks, with a specific accent on electrical storage mechanisms. By evaluating interactions between renewable sources such as wind and solar, storage units, predominantly battery-based, and diverse loads like buildings and transportation, an integrated model is proposed. Both the first and second laws of thermodynamics are imposed as constraints on the MES operations within these networks. The effect of these thermodynamic laws, intertwined with electrical storage tactics, on overall thermodynamic efficiency is extensively detailed. Preliminary results have shown that, under certain circumstances, the adoption of well-defined source-storage-load synergistic strategies within distribution networks can significantly amplify the system's operational efficiency whilst maintaining a consistent energy supply. The insights derived from this investigation provide invaluable guidance to both designers and decision-makers in the realm of multi-energy systems within distribution networks, propelling the investigative nexus between thermodynamics and energy distribution systems.