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

TL;DR

The paper addresses how to generate the cosmic baryon asymmetry when the source of baryon-number violation is a time-dependent, zero-mean chemical potential, showing that adiabatic cancellation suppresses such oscillatory drives under smooth freeze-out. It derives a transfer-function bound with a low-pass form $F(x)=1/sqrt{1+x^2}$, $x=omega*tau_off$, capturing the suppression and identifying the key parameter $\omega\tau_{off}$. To overcome this suppression, it introduces an entropy-clock mechanism where $\mu_B = \epsilon \; d\ln S/dt$ ties the bias to irreversible entropy production during reheating, yielding a sign-definite, DC component via the overlap integral $\Pi_{eff}$. In the overlap framework, the observed yield is $n_B/s = K \epsilon \Pi_{eff}$ with an overlap temperature $T_{ov}$, and a minimal Weinberg-operator benchmark places $T_F \sim 10^{12}$--$10^{13}$ GeV with $\epsilon \Pi_{eff}$ of order $10^{-3}$ to reproduce the observed $n_B/s \simeq 8.7\times 10^{-11}$; the framework offers falsifiable connections to reheating dynamics and neutrino masses through gravitational-wave constraints and cosmology.

Abstract

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.

Figures (3)

• Figure 1: Toy-model low-pass transfer function $F(x)=1/\sqrt{1+x^2}$ with $x\equiv \omega\tau_{\rm off}$, illustrating adiabatic cancellation for a smoothly switched-off oscillatory source.
• Figure 2: Numerical solution during reheating. (a) Evolution of inflaton ($\rho_\phi$) and radiation ($\rho_R$) energy densities with the resulting asymmetry yield (right axis); the dashed line marks the observed baryon asymmetry. (b) Frozen asymmetry versus freeze-out temperature for two reheating temperatures; the observed band is reproduced when $T_F$ falls in the Weinberg-operator range for $T_R\sim 10^{10}$--$10^{11}$ GeV and $\epsilon\sim 1$.
• Figure 3: Illustration of the overlap formulation: baryon-violation window $W(t)$ and entropy-production pulse $\Pi(t)$. The shaded region corresponds to $\Pi_{\rm eff} = \int dt\, W(t)\Pi(t)$. Inset: required $\epsilon\Pi_{\rm eff}$ vs. overlap temperature from Eq. (6) of the main text.