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 $P=-B/{\rho }^{\alpha }$, where $B=B_0{V}^{n/3}$. The model includes a bulk-viscous pressure $\Pi =-3\xi H$, with $\xi ={\xi }_0{\rho }^{1/2}$. We find that the physically viable branch corresponds to ${\xi }_0<0$, 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 ${\xi }_0<0$. The entropy vanishes as $T\to 0$, 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 $\alpha =0.0024$, $n=-0.0182$, and ${\xi }_0=-0.0015$, 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.

27 pages, 10 figures