A Description of Laser Stability near Threshold by Liapounov’s Second Method

  • Adi R. Bulsara
  • William C. Schieve
Conference paper


The theory of the generalized entropy developed by Prigogine, George and Henin [1] in Brussels and Austin suggests a form for an N-body Liapounov function which has already been discussed for closed systems [2–4]. Starting from the Liouville-von Neumann equation for the density operator ρ, Prigogine introduces a causal or physical particle representation wherein he defines a “physical” density matrix ρ(P) which is generated from ρ by a non-unitary transformation in strongly coupled system., this representation, the retarded and advanced components of ρ(P) obey separate evolution equations. For weakly coupled systems, ρ(P) reduces to the untransformed ρ which is a solution to the Pauli equation. This theory has been applied by Hubert [5] to a dense hard sphere gas obeying the Enskog equation. Further, Bulsara and Schieve have demonstrated [2] that infinitesimally close to thermal equilibrium, the generalized form of the entropy proposed by Prigogine et al. has the same form as the Liapounov function referred to above, for weakly coupled systems, a fact which we shall exploit in section 5 of this paper.


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Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • Adi R. Bulsara
    • 1
  • William C. Schieve
    • 1
  1. 1.University of TexasAustinUSA

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