Energy Conservation and Time-Reversal Symmetry Breaking in the K-Kernel Framework

This paper investigates the thermodynamic implications of the K-Kernel framework. We demonstrate that the spacetime fabric acts as a non-Markovian memory reservoir, storing energy from past states. By comparing classical energy conservation (E = T + V) with the managed spacetime energy (E = T + V + gamma*M(t)), we show that the introduction of memory fundamentally breaks time-reversal symmetry. This provides a deterministic physical mechanism for the 'Arrow of Time', where the system retains a historical dependence on its past. We also prove that the memory functional remains bounded, ensuring strict passivity and preventing energy blow-up.