When the entropy has no maximum: A new perspective on the instability of the first-order theories of dissipation

Understand

The first-order relativistic fluid theories of dissipation proposed by Eckart and Landau-Lifshitz have been proved to be unstable.

• They admit solutions which start in proximity of equilibrium and depart exponentially from it.
• We show that this behaviour is due to the fact that the total entropy of these fluids, restricted to the dynamically accessible states, has no upper bound.
• As a result, these systems have the tendency to constantly change according to the second law of thermodynamics and the unstable modes represent the directions of growth of the entropy in state space.