Analogous to the HR diagram for stars, the thermal equilibrium curve encodes the thermodynamics of accretion disks by expressing the local balance between heating---primarily via viscous dissipation---and cooling---typically through radiative transfer. These curves are commonly plotted as surface density versus effective temperature.
When an S--shaped profile appears, the annular thermal equilibria become bistable, and limit-cycle oscillations arise when the external mass accretion rate falls within a certain range. This behavior underpins the disk instability model for recurring outbursts in cataclysmic binaries. In this paper, first-principles thermal equilibrium curves for accretion disks driven by magnetorotational instability (MRI) are presented. Unlike the parameterized $\alpha$-viscosity approach, the curves are obtained by directly solving the governing equations with radiation--magnetohydrodynamics simulations, thereby reproducing S--shaped loci without prescribing $\alpha$.
A brief review is also provided of the disk instability in dwarf-nova systems and of the origin of shear stresses (via MRI). Notes on the stability of radiation--dominated accretion flows are included in the Appendix.