2026/08/05 by Imtiaz Khan, G. Mustafa, Chengxun Yuan +3
Physics and Astronomy · #hep-ph
10 pages, 6 figures
arxiv created 2026/08/05 · arxiv updated 2026/08/06
Thermal alignment cannot be inferred from the axion mean alone because the dissipative bath that erases the initial displacement also prepares field and momentum fluctuations. We derive a phase space covariance bound that quantifies this memory and noise relation in the full inertial Langevin system. A renormalizable finite temperature gauge theory then links the temporary susceptibility, the Chern-Simons bath, bath termination, and the stable late potential through one scalar transition. Solving the coupled mean and covariance evolution demonstrates erasure of the incoming state, release of a causal infrared spectrum, and capture of the full phase space distribution as axion dark matter across the transition interval. Thermal alignment therefore determines a calculable late axion state rather than a homogeneous displacement alone.