The Hydraulic Arrow of Time: Chronology Protection and Entropy Generation via Irreversible Flux Injection

We address the origin of the temporal asymmetry (Arrow of Time) within the context of Open System Cosmology. Standard cosmological models assume microscopic time reversal symmetry (CPT invariance), making the macroscopic arrow of time a statistical emergence (Boltzmann's H-theorem). In contrast, we propose that time is a Hydrodynamic Variable driven by a fundamental Flux Injection from a precursor manifold. In this view, the expansion of spacetime is not inertial but driven by a pressure gradient. This imposes a fundamental directionality: the "Future" is defined as the direction of volume increase driven by injection. We link this mechanism to the Quantum Measurement Problem: wavefunction collapse is irreversible because the information shed into the bulk geometry during decoherence is carried away by the expansion flow, becoming causally irretrievable. Finally, we derive a Hydraulic Chronology Protection Mechanism. Closed Timelike Curves (time travel) are forbidden not merely by abstract geometry, but by the energy density of the flux itself. Reversing local time would require generating a pressure exceeding the injection pressure of the Big Bang, which is energetically impossible for any sub-universal machine.