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 In ρ can provide a Lyapunov criterion for the stability of thermodynamic equilibrium. A conjecture on a special positive-definiteness property of - k Tr ρ In ρ remains to be proved. © 1985 American Institute of Physics.

A theorem on Lyapunov stability for dynamical systems and a conjecture on a property of entropy

BERETTA, Gian Paolo
1986-01-01

Abstract

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 In ρ can provide a Lyapunov criterion for the stability of thermodynamic equilibrium. A conjecture on a special positive-definiteness property of - k Tr ρ In ρ remains to be proved. © 1985 American Institute of Physics.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/161317
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