
VOLUME 118 (2023)  ISSUE 4 
PAGE 280

Analog Sommerfeld law in quantum vacuum
G. E. Volovik
Low Temperature Laboratory, Aalto University, P.O. Box 15100, FI00076 Aalto, Finland Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia
Abstract
The activation temperature T in the de Sitter environment is twice
larger than 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 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.

