Gravitational Baryogenesis from Entropy Production and Parity Violation: A Unified Framework

We present a unified framework for gravitational baryogenesis combining two mechanisms: (i) an entropy-clock source that generates a sign-definite baryon chemical potential mu_B proportional to d ln S/dt during irreversible entropy production, and (ii) CP violation from a gravitational theta term theta R Rtilde analogous to the QCD vacuum angle. The entropy-clock evades adiabatic cancellation that suppresses purely oscillatory chemical potentials under smooth freeze-out; we quantify this with a universal low-pass transfer function F(x)=1/sqrt(1+x^2), where x=omega*tau_off. A minimal UV completion via a dilaton coupled to the conformal anomaly yields the entropy-clock coupling with decay constant f_sigma ~ 10^17-10^18 GeV. The theta term provides CP violation through interference between topologically distinct gravitational configurations; we estimate an instanton suppression factor kappa_inst ~ 10^-2-10^-1. The combined mechanism predicts Y_B ~ c*kappa*Pi_eff*epsilon_eff, linking the baryon asymmetry to the reheating temperature, the theta angle, and the entropy-production history. For Loop Quantum Cosmology bounces we derive an analytic expression for the circular polarization of the stochastic gravitational-wave background, with |Pi| ~ pi*|theta| for horizon-crossing modes, potentially testable by future space-based detectors.