Ship subsystems and mission modules perform energy conversion during their operation resulting in a combination of electricity consumption, heat generation and mechanical work. These multi-physics subsystems often have opportunities for performing an energy storage role during their operation cycle. The kinetic energy stored in the rotating mass of a generator set or the electrical energy stored in a railgun pulse forming network are but two examples of energy storage aboard warships. Treating each subsystem as a disconnected entity reduces the potential for exploiting their inherent interactions and results in over-designed shipboard systems with excessive weight and volume. Exergy - the amount of energy available for performing useful work - provides a path for exploiting multi-physics energy flows. Utilizing the Second Law of Thermodynamics, by modeling and minimizing exergy destruction, a recent study, showed that exergy control increased the overall efficiency by 18% over traditional optimization techniques when applied to a terrestrial HVAC application. In this paper a notional, multi-physics ship power system is developed that explicitly captures the exergy flows. Particular attention is given to exergy destruction phenomena. Simulation of the system illustrates operational characteristics with greatest impact on exergy destruction highlighting areas for applying optimal, exergy-based control schemes. This approach will allow ship designers to minimize the size and weight of installed power generation, energy storage and thermal management systems, enabling the affordable implementation of advanced weapons and sensors.