Low coronal highly anisotropic structures as loops and prominences are relatively stable configurations with densities hundreds of times higher and temperatures hundreds of times lower than their surrounding corona. Magnetohydrodynamics (MHD) open systems, generally driven by coupled mechanical and thermal perturbations, can go beyond the linear state configurations into new stationary states known as nonlinear equilibria. Thus, a crucial requirement for any theoretical model that intends to describe these far-from-equilibrium states is to give an account of the stability and evolution of the numerous nonlinear thermodynamic stationary states that can arrive. Observations obtained with high spatial and time resolution instruments of the new spacecraft generation describe a wide spectrum of configurations which sustain fast and slow magnetoacoustic oscillations or propagating MHD waves that are ducted by the magnetic fields of the low β-corona media. Measurements of characteristic periods, speeds and damping times as well as different theoretical models that intend to describe non-dissipative damping mechanisms and leakage processes of systems with high-Reynolds number provide us with new diagnostic tools to reveal unknown or more accurate solar physics parameters. We summarize some theoretical and observational results that give an account of the coronal seismology state-of-art. We present a thermodynamic stability criterion to describe the modes and stability of coronal structures. We give some results of its application to coronal seismology. This allows us to discuss the feasibility of wave- and flow-based models for solar loops and to offer a different explanation to the presence of frequencies associated with helioseismological p-modes at the altitude of the corona.