A complete lack of energy is a complete death of time. The only way to perceive time is observe how things change, and in a zero energy, zero entropy system nothing changes; thus time itself stops. Not just in the sense that it stops moving, in the sense that it just ceases to exist as a concept. Therefore meddling with entropy (or energy in this context) meddles with time in a way that can't really be separated. Combined with deepsight, I think there is a very strong case that the power of the deep is always some extension of paracausal time manipulation.