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 $I_\varphi(x)=(\cos\varphi-x\sin\varphi)/(1+x^2)$ and the phase-optimized envelope is $F_{\rm amp}(x)=1/\sqrt{1+x^2}$, with $x=\omega\tau_{\rm off}$. 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, $\theta_X=\epsilon_X\ln(S/S_0)$, giving $\mu_X=\epsilon_X d\ln S/dt$ during entropy-producing reheating; the yield equation includes entropy dilution. During perturbative matter-dominated reheating, $S\propto a^{15/8}$ and $\Pi=d\ln S/d\ln a=15/8$ before completion. Successful freeze-out requires overlap between entropy production and charge violation. In a Weinberg-operator $B-L$ benchmark this selects $T_R={\cal O}(T_F)$, with $T_F\sim10^{12}$--$10^{13}\,\mathrm{GeV}(0.05\,\mathrm{eV}/\bar m_\nu)^2$. 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, $|\epsilon_X\Pi_{\rm eff}|\simeq3.2\times10^{-3}(10^{12}\,\mathrm{GeV}/T_{\rm ov})$; sphaleron reprocessing of a $B-L$ source increases this by $79/28$. With $\Pi=15/8$, this gives $|\epsilon_X|\zeta\simeq1.7\times10^{-3}$ and $4.8\times10^{-3}$, respectively, at $T_{\rm ov}=10^{12}\,\mathrm{GeV}$. 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.