The Arrow of Time as Pe Gradient Direction: Time-Reversal Symmetry at Pe less than 1, Entropy Production at Pe greater than 1, and the Derivation of Temporal Directionality from Void Framework Transport Dynamics

Derives the thermodynamic arrow of time from Pe gradient direction, demonstrating that time-reversal symmetry holds exactly at Pe less than 1 (the COHERENT regime, confirmed by the CPT theorem in quantum systems), breaks at the Pe=1 crossing (decoherence as phase transition), and that entropy production is Pe monotonicity. The Big Bang initial condition is derived as Pe=0, not postulated. The Crooks fluctuation theorem provides closed-form confirmation: P(forward)/P(reverse) = exp(Pe). Spearman convergence across N=12 substrates from quantum systems to macroscopic irreversible processes.