The entropy principle shows that, for self-gravitating perfect fluid, the Einstein field equations can be derived from the extrema of the total entropy, and the thermodynamical stability criterion are equivalent to the dynamical stability criterion. In this paper, we recast the dynamical criterion for the charged self-gravitating perfect fluid in Einstein–Maxwell theory, and further give the criterion of the star with barotropic condition. In order to obtain the thermodynamical stability criterion, first we get the general formula of the second variation of the total entropy for charged perfect fluid case, and then obtain the thermodynamical criterion for radial perturbation. We show that these two stability criterions are the same, which suggest that the inherent connection between gravity and thermodynamic even when the electric field is taken into account.

熵原理表明，对于自引力完美流体，可以从总熵的极值推导出爱因斯坦场方程，热力学稳定性判据等价于动力学稳定性判据。在本文中，我们重新制定了爱因斯坦-麦克斯韦理论中带电自引力完美流体的动力学判据，并进一步给出了恒星具有正压条件的判据。为了得到热力学稳定性判据，首先得到带电完全流体情况下总熵的二次变分的通式，然后得到径向扰动的热力学判据。我们证明这两个稳定性标准是相同的，