A theorem on Lyapunov stability for dynamical systems and a conjecture on a property of entropy
A theorem on Lyapunov stability for dynamical systems and a conjecture on a property of entropy
For a general dynamical system, it is proved that an equilibrium state belonging to a continuous family of conditionally stable equilibrium states is stable. The result is applied to quantum thermodynamics to clarify in what restricted sense the entropy functional s( ρ)=−k Tr ρ ln ρ can provide a Lyapunov …