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

Abstract

We formulate a transfer test for baryogenesis driven by time-dependent derivative sources. A zero-mean oscillatory chemical potential convolved with a smooth finite-time kernel is low-pass filtered. For a one-sided exponential effective kernel, the signed response is $I_{\ddot{I}}†(x)=(\cos \ddot{I}†-x\sin \ddot{I}†)/(1+x^2)$ and the phase-optimized envelope is $F_{\mathrm{amp}}(x)=1/\sqrt{1+x^2}$, with $x=\ddot{I}‰\ddot{I}{„}_{\mathrm{off}}$. Its sharp onset gives a $1/x$ high-frequency tail; smoother turn-ons can suppress more strongly. An integration-by-parts bound shows that rapidly sign-changing sources are controlled by their residual low-frequency component. We then study an entropy-clock ansatz, $\hat{I}{¸}_X=\hat{I}{\mu }_X\ln (S/S_0)$, giving $\hat{I}{¼}_X=\hat{I}{\mu }_{X}d\ln S/dt$ during entropy-producing reheating; the yield equation includes entropy dilution. During perturbative matter-dominated reheating, $S\propto a^{15/8}$ and $\hat{I}=d\ln S/d\ln a=15/8$ before completion. Successful freeze-out requires overlap between entropy production and charge violation. In a Weinberg-operator $B-L$ benchmark this selects $T_R=\mathcal{O}(T_F)$, with $T_F\sim 10^{12}$--$10^{13}\mathrm{GeV}(0.05\mathrm{eV}/{\bar{m}}_{\hat{I}}½{)}^2$. If $T_R\gg T_F$, the source ends before freeze-out and is washed out; if $T_R\ll T_F$, the interaction is never efficient during reheating. For a direct baryon source, $|\hat{I}{\mu }_X{\hat{I}}_{\mathrm{eff}}|\simeq 3.2\times 10^{-3}(10^{12}\mathrm{GeV}/T_{\mathrm{ov}})$; sphaleron reprocessing of a $B-L$ source increases this by $79/28$. With $\hat{I}=15/8$, this gives $|\hat{I}{\mu }_X|\hat{I}\P \simeq 1.7\times 10^{-3}$ and $4.8\times 10^{-3}$, respectively, at $T_{\mathrm{ov}}=10^{12}\mathrm{GeV}$. The entropy-clock source is phenomenological; a UV completion must explain why the charge-biasing variable tracks $\ln S$ or an equivalent monotonic dissipative variable.

9 pages, 3 figures. Revised entropy dilution, phase-resolved transfer response, reheating/freeze-out consistency, endpoint regularity, sphaleron normalization, sign conventions, and literature positioning