Note on the chemical potential of decoupled matter in the Universe

2011/08/30 by Theo M. Nieuwenhuizen, Nieuwenhuizen, Theo M., Claudia Pombo +1
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Statistical Mechanics (cond-mat.stat-mech) #astro-ph.CO #cond-mat.stat-mech #gr-qc

paper · pdf · doi:10.48550/arxiv.1109.0487

4 pages latex

arxiv created 2011/08/30 · openalex publication_date 2011/08/30 · arxiv updated 2011/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Textbooks on cosmology exhibit a thermodynamic inconsistency for free streaming, decoupled matter. It is connected here to the chemical potential, which deviates from its equilibrium value μ=αk_BT, where α is the usual parameter of the Fermi-Dirac or Bose-Einstein distribution function.

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