## 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: {gamma}({bold v}{sup 2}/{ital c}{sup 2}{sub {ital s}}){minus}1 {lt}{ital d}ln{ital T}/{ital d}ln{ital n}{lt}{gamma}{minus}1 for each species, where {gamma} is the adiabatic index and {ital c}{sub {ital s}} the sound speed. Somemore »