Analog of the Sommerfeld Law in Quantum Vacuum
Abstract
The activation temperature T in the de Sitter environment is twice the GibbonsHawking temperature, related to the cosmological horizon. We consider the activation temperature as the local temperature of the de Sitter vacuum, and construct the local thermodynamics of the de Sitter state. This thermodynamics includes also the gravitational coupling K and the scalar Riemann curvature $R$ as the thermodynamically conjugate variables. These variables modify the thermodynamics of the GibbsDuhem relation in the de Sitter state. The free energy density is proportional to $  {{T}^{2}}$, which is similar to that in the nonrelativistic Fermi liquids and in relativistic matter with equation of state $w = 1$. The local entropy is proportional to the local temperature, while the total entropy inside the cosmological horizon is $A{/}4G$, where A is the area of the horizon. This entropy is usually interpreted as the entropy of the cosmological horizon. We also consider the possible application of the de Sitter thermodynamics to the Schwarzschildde Sitter black hole and to black and white holes with the de Sitter cores.
 Publication:

Soviet Journal of Experimental and Theoretical Physics Letters
 Pub Date:
 August 2023
 DOI:
 10.1134/S0021364023602208
 arXiv:
 arXiv:2307.00860
 Bibcode:
 2023JETPL.118..282V
 Keywords:

 General Relativity and Quantum Cosmology;
 Condensed Matter  Other Condensed Matter;
 High Energy Physics  Phenomenology
 EPrint:
 8 pages, no figures, title changed, version accepted in JETP Letters