https://doi.org/10.1140/epjc/s10052-025-13754-5
Regular Article - Theoretical Physics
Holographic thermodynamic relation for dissipative and non-dissipative universes in a flat FLRW cosmology
Department of Mechanical Systems Engineering, Kanazawa University, Kakuma-machi, 920-1192, Kanazawa, Ishikawa, Japan
Received:
23
November
2024
Accepted:
28
December
2024
Published online:
20
January
2025
Horizon thermodynamics and cosmological equations in standard cosmology provide a holographic-like connection between thermodynamic quantities on a cosmological horizon and in the bulk. It is expected that this connection can be modified as a holographic-like thermodynamic relation for dissipative and non-dissipative universes whose Hubble volume V varies with time t. To clarify such a modified thermodynamic relation, the present study applies a general formulation for cosmological equations in a flat Friedmann–Lemaître–Robertson–Walker (FLRW) universe to the first law of thermodynamics, using the Bekenstein–Hawking entropy and a dynamical Kodama–Hayward temperature
. For the general formulation, both an effective pressure
of cosmological fluids for dissipative universes (e.g., bulk viscous cosmology) and an extra driving term
for non-dissipative universes (e.g., time-varying
cosmology) are phenomenologically assumed. A modified thermodynamic relation is derived by applying the general formulation to the first law, which includes both
and an additional time-derivative term
, related to a non-zero term of the general continuity equation. When
is constant, the modified thermodynamic relation is equivalent to the formulation of the first law in standard cosmology. One side of this modified relation describes thermodynamic quantities in the bulk and can be divided into two time-derivative terms, namely
and
terms, where
is the mass density of cosmological fluids. Using the Gibbons–Hawking temperature
, the other side of this relation,
, can be formulated as the sum of
and
, which are equivalent to the
and
terms, respectively, with the magnitude of the
term being proportional to the square of the
term. In addition, the modified thermodynamic relation for constant
is examined by applying the equipartition law of energy on the horizon. This modified thermodynamic relation reduces to a kind of extended holographic-like connection when a constant
universe (whose Hubble volume varies with time) is considered. The evolution of thermodynamic quantities is also discussed, using a constant
model, extending a previous analysis (Komatsu in Phys Rev D 108:083515, 2023).
© The Author(s) 2025
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