Thermodynamic Stability of a Viscous Variable Generalised Chaplygin Gas
Abstract
We investigate the cosmological dynamics and thermodynamic properties of a viscous variable generalized Chaplygin gas (VVGCG) model in a spatially flat Friedmann--Lema^ıtre--Robertson--Walker universe, described by P=−B/ρα, where B=B0Vn/3. The model includes a bulk-viscous pressure Π=−3ξH, with ξ=ξ0ρ1/2. We find that the physically viable branch corresponds to ξ0<0, for which the positive viscous pressure dominates at early times, producing decelerated expansion. As the volume increases, the effective pressure changes sign at a finite volume Vc, while the transition to acceleration occurs at a larger volume Vf. At large volume, the equation-of-state parameter approaches a phantom-like regime for n<0. A detailed thermodynamic analysis of the thermal and caloric equations of state, entropy, heat capacity, and isothermal and adiabatic stability shows that the stability conditions and cV>0 are simultaneously satisfied for n<0 and ξ0<0. The entropy vanishes as T→0, consistent with the third law, while the model admits a finite minimum volume and corresponding maximum temperature. Thermodynamic consistency is further verified through the fundamental thermodynamic identity. The framework also contains several existing Chaplygin-gas models as special cases. Constraints from the Hubble-57 data yield α=0.0024, n=−0.0182, and ξ0=−0.0015, consistent with the thermodynamically stable parameter region. Thus, the VVGCG model provides a consistent description of cosmic evolution from an early decelerating phase to late-time phantom-like acceleration while remaining thermodynamically stable throughout the evolution.
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BibTeX
@misc{panigrahi2026thermodynamic,
title = {{Thermodynamic Stability of a Viscous Variable Generalised Chaplygin Gas}},
author = {D. Panigrahi and K. Kanjilal and Saibal Ray},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05361},
eprint = {2610.05361},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05361},
}
RIS
TY - UNPB
TI - Thermodynamic Stability of a Viscous Variable Generalised Chaplygin Gas
AU - D. Panigrahi
AU - K. Kanjilal
AU - Saibal Ray
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05361
UR - https://arxiv.org/abs/2610.05361
AB - We investigate the cosmological dynamics and thermodynamic properties of a viscous variable generalized Chaplygin gas (VVGCG) model in a spatially flat Friedmann--Lema^ıtre--Robertson--Walker universe, described by P=−B/ρ^α, where B=B_0V^n/3. The model includes a bulk-viscous pressure Π=−3ξH, with ξ=ξ_0ρ^1/2. We find that the physically viable branch corresponds to ξ_0<0, for which the positive viscous pressure dominates at early times, producing decelerated expansion. As the volume increases, the effective pressure changes sign at a finite volume V_c, while the transition to acceleration occurs at a larger volume V_f. At large volume, the equation-of-state parameter approaches a phantom-like regime for n<0. A detailed thermodynamic analysis of the thermal and caloric equations of state, entropy, heat capacity, and isothermal and adiabatic stability shows that the stability conditions and c_V>0 are simultaneously satisfied for n<0 and ξ_0<0. The entropy vanishes as T→0, consistent with the third law, while the model admits a finite minimum volume and corresponding maximum temperature. Thermodynamic consistency is further verified through the fundamental thermodynamic identity. The framework also contains several existing Chaplygin-gas models as special cases. Constraints from the Hubble-57 data yield α=0.0024, n=−0.0182, and ξ_0=−0.0015, consistent with the thermodynamically stable parameter region. Thus, the VVGCG model provides a consistent description of cosmic evolution from an early decelerating phase to late-time phantom-like acceleration while remaining thermodynamically stable throughout the evolution.
ER -