  We have applied thermodynamic stability analysis to derive the stability and
causality conditions for conventional relativistic viscous hydrodynamics and
spin hydrodynamics. We obtain the thermodynamic stability conditions for
second-order relativistic hydrodynamics with shear and bulk viscous tensors,
finding them identical to those derived from linear mode analysis. We then
derive the thermodynamic stability conditions for minimal causal extended
second-order spin hydrodynamics in canonical form, both with and without
viscous tensors. Without viscous tensors, the constraints from thermodynamic
stability exactly match those from linear mode analysis. In the presence of
viscous tensors, the thermodynamic stability imposes more stringent constraints
than those obtained from linear mode analysis. Our results suggest that
conditions derived from thermodynamic stability analysis can guarantee both
causality and stability in linear mode analysis.
