Matter‑Sector Kinetic Freeze‑Out in Degenerate Fermionic Systems

The thermodynamic arrow of time and the timing of entropy production in cosmology depend not only on global initial conditions but also on the transport properties of individual subsystems. In this work, we investigate whether a highly degenerate fermionic matter sector can enter a kinetic regime in which Pauli blocking suppresses collision‑driven momentum redistribution over a finite cosmological interval. The analysis is formulated strictly at the level of subsystem transport rather than as a complete cosmological model. Starting from exact zero‑temperature ideal Fermi‑gas relations, we derive the Fermi momentum, internal energy, and degeneracy pressure, and embed the transport problem in the relativistic Boltzmann–Uehling–Uhlenbeck framework in a Friedmann–Robertson–Walker background. The coupled fermion–boson quantum Boltzmann system is constructed explicitly, including the competing effects of fermionic exclusion and Bose‑enhanced washout channels. A precise transport‑level definition of matter‑sector kinetic freeze‑out is introduced, based on the suppression of momentum redistribution relative to the Hubble expansion rate. A closure‑level benchmark estimate is then developed for a heavy‑mediator effective interaction. This estimate illustrates how Pauli blocking, Hubble expansion, and bosonic washout compete parametrically and identifies representative crossing scales in the visible sector. The benchmark is emphasized to be illustrative rather than decisive: it does not substitute for a momentum‑resolved solution of the coupled collision problem and does not by itself establish cosmological viability. The principal result of the manuscript is to clarify the transport logic and scaling structure underlying matter‑sector kinetic freeze‑out. Exact results are confined to the ideal Fermi‑gas relations and the kinematic structure of the collision operator, while conclusions regarding cosmological persistence are conditional on explicit assumptions about degeneracy, mediator hierarchy, and bosonic occupation. The analysis identifies the decisive next step as a momentum‑resolved numerical solution of the coupled fermion–boson transport equations and the propagation of the resulting phase‑space distributions to cosmological observables such as radiation density and free‑streaming scales. This preprint establishes a precise transport framework for assessing kinetic bottlenecks in degenerate fermionic matter and provides a controlled basis for evaluating whether such regimes can arise in consistent cosmological settings.