Baryogenesis from the Thermodynamic Arrow of Time: a Transfer-Function Bound and an Entropy-Clock Mechanism

We establish a quantitative statement: baryogenesis driven by a purely oscillatory (zero-mean) chemical potential is parametrically suppressed under smooth freeze-out (adiabatic cancellation). A simple toy model yields an analytic low-pass transfer function F(x)=1/sqrt(1+x^2), with x = omegatau_off, capturing the suppression for omegatau_off >> 1. We then propose an "entropy clock" source tied to thermodynamic irreversibility: during reheating the growth of comoving entropy S = a^3 s generates a sign-definite chemical potential mu_B = epsilon * d log S/dt that drives spontaneous baryogenesis. The final asymmetry reduces to an overlap integral Pi_eff = integral dt W(t) Pi(t) between the violation window W(t) and entropy production Pi(t)= d log S/dt. As a minimal benchmark, Delta L=2 scatterings from the Weinberg operator yield T_F ~ 10^12-10^13 GeV for m_nu ~ 0.05 eV, requiring epsilonPi_eff ~ few x 10^-3.