in a quasistatic process is written in the following form: $$\delta m = -\omega \delta\varphi_0 + \mu_{eff} \delta N,$$ where by “quasistatic process” we mean successive changes among the infinitesimally nearby equilibrium solutions.

Suppose that the isolated neutron star is perturbed slightly with $\varphi_0$ and $N$ constant for some reason other than incident waves, while spherical symmetry is preserved. Then the outgoing waves can carry out some positive energy to infinity and the system cannot keep its original state if there exists an energetically favorable configuration which is infinitesimally deformed from the system with the same $\varphi_0$ and $N$. Therefore, an equilibrium solution $X$ is secularly stable against spherically symmetric (infinitesimal) perturbations if and only if there is no momentarily static and spherically symmetric configuration $Y$ which is arbitrarily close to $X$ with the same $\varphi_0$ and $N$ but strictly smaller $m$.

In order to examine the stability of the equilibrium solution, we follow the turning point method [@katz1978; @katz1979; @sorkin1981; @sorkin1982]. In the present problem, $m$ is a potential function, since the equilibrium solution is a stationary point of $m$ ($\delta m=0$) and the stable equilibrium solution is a minimal point of $m$ ($\delta m=0$ and $\delta^2 m >0$). 