^{1,2}

^{*}

^{1}

^{†}

^{1}

^{‡}

wojciech.florkowski@ifj.edu.pl

avdhesh.kumar@ifj.edu.pl

radoslaw.ryblewski@ifj.edu.pl

^{3}.

We apply the convection stability criterion to a fluid in global thermodynamic equilibrium with a rigid rotation or with a constant acceleration along the streamlines. Different equations of state describing strongly interacting matter are considered, and for each of them the analyzed system is found to be stable with respect to convection. This finding brings new evidence for physical relevance of nonstatic global equilibrium states. Our results can be directly used for other similar media to check their convective stability.

If the entropy per particle decreases with increasing altitude in Earth's atmosphere, the latter becomes convectively unstable

In this Rapid Communication we analyze the problem of convective stability of a relativistic fluid in global thermodynamic equilibrium (GTE) with a rigid rotation or with a constant local acceleration along the streamlines. Throughout the text we neglect the effects of gravity. The GTE with rotation has brought a lot of attention in the past years as in most cases the rigid rotation implies the spin polarization of particles forming the fluid (due to the spin-orbit interaction). Such a polarization-vorticity coupling forms nowadays the basis for explanation of the heavy-ion data showing nonzero global polarization of the ^{1}

Although in the GTE with rotation we deal with centripetal acceleration, by the GTE with acceleration we mean here only the case with a constant local acceleration of fluid elements along the streamlines.

has become also interesting latelyNonstatic global equilibria with rotation and acceleration are interesting

^{2}

We use natural units with

The GTE conditions for

From Eq. ^{3}

Other possible forms of the flow in global equilibrium with acceleration correspond to a translation of the

Using the thermodynamic identity ^{4}

The specific-heat

Let us come back to the discussion of the GTE. In this case the fluid's acceleration as well as its temperature and chemical potential are known, hence, the convection stability condition can be directly applied. Using Eqs.

For conformal systems the trace of the energy-momentum tensor vanishes, hence

In Figs.

The coefficient

The coefficient

Studying the systems described by Eqs.

For

Another simple equation of state that can be analyzed analytically has the form

The two schematic equations of state discussed earlier may be valid at very high temperatures. In order to analyze realistic equations of state we consider now the ideal hadron gas (HG) model with the input defined by the ^{5}

The coefficient

As yet another equation of state we use the result of Refs.

The coefficient