On phantom thermodynamics with negative temperature

We discuss the thermodynamic properties of the Friedmann–Robertson–Walker universe with dark energy fluids labelled by ω=p/ρ<−1/3$\omega =p/\rho <-1/3$. Using the integrability condition, we show that the phantom phase of ω<−1$\omega <-1$ can still be thermodynamically allowed even when the temperature takes on negative values because in that case, there exists at least a condition of keeping physical values for p and ρ.