Lyapunov stability and thermal stability of partially relaxed fluids and plasmas

The relation between the Lyapunov stability of a Hamiltonian system and the thermal stability of a fluid whose temperature is controlled from outside is explored: The free energy as a functional of the correct variables (specific volume, local entropy, and some Clebsch potentials of the velocity) may serve as a Lyapunov functional, depending on the open-quote open-quote Casimirs close-quote close-quote as exchanged quantities. For a multi-species plasma one obtains a sufficient condition for stability: γ(v2/c2s)-1 <dlnT/dlnn<γ-1 for each species, where γ is the adiabatic index and cs the sound speed. Some features of partially relaxed (T=const) cylindrical plasmas are also discussed. copyright 1996 American Institute of Physics