Thermodynamic Analyses of Laser Instability and Superradiance

  • H. Hasegawa
  • S. Sawada
  • M. Mabuchi
Conference paper


The instability phenomena in nonlinear optics, laser and super-radiance, have received the interest of theoretical investigation from a macroscopic point of view. In the Third Rochester Conference, Graham discussed[1] the problem of unifying the laser theory and the non-equilibrium thermodynamic theory of Glansdorff and Prigogine,[2] based on the entropy expression for the steady non-equilibrium state, S = lnP, where P is the well-established steady-state solution of the laser Fokker-Planck equation.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Graham, in Coherence and Quantum Optics, edited by L. Mandel and E. Wolf ( Plenum Press, New York, 1973 ) p. 851.CrossRefGoogle Scholar
  2. 2.
    P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stabiltiy and Fluctuations ( Wiley-Interscience, London, 1971 ).Google Scholar
  3. 3.
    H. Hasegawa, Prog. Theor. Phys. 56, 44 (1976); 57, 1523 (1977); 58, No. 1 (1977); see also Phys. Lett. 60A, 171 (1977).Google Scholar
  4. 4.
    G. Nicolis, in Advances in Chemical Physics, XIX, edited by I. Prigogine and S.O. Rice ( Wiley-Interscience, London, 1971 ) p. 209.CrossRefGoogle Scholar
  5. 5.
    L. Onsager, Phys. Rev. 37, 405 (1931).ADSCrossRefGoogle Scholar
  6. 6.
    Non-Equilibrium Thermodynamics Variational Techniques and Stability, edited by Donnelly, Hermann and Prigogine (The University of Chicago Press, Chicago and London, 1965).Google Scholar
  7. 7.
    H. Risken, in Progress in Optics, Vol. 8, edited by E. Wolf ( North-Holland, Amsterdam, 1970 ) p. 239.Google Scholar
  8. 8.
    R. Bonifacio, P. Schwendimann and F. Haake, Phys. Rev. A 4, 854 (1971).ADSCrossRefGoogle Scholar
  9. 9.
    R. Kubo, K. Matsuo and K. Kitahara, J. Stat. Phys. 9, 51 (1973);Google Scholar
  10. M. Suzuki, Physica 84A, 48 (1976);ADSCrossRefGoogle Scholar
  11. Prog. Theor. Phys. 57, 380 ( 1977 );Google Scholar
  12. T. Arimitsu and M. Suzuki, to be published (1977).Google Scholar
  13. 10.
    F. Hofflich, Z. Physik 226, 395 (1969).ADSCrossRefGoogle Scholar
  14. 11.
    This statement deserves a careful account of its implication, which we point out here in order to avoid any misleading reference to the Glansdorff -Prigogine original expression,[2]: As noted by these authors, the inequality guarantees that (d/dt)(JμXμ) ≤ 0in the near steady-state for which Jμ=Lμ⋁X (Lμv=L and constant), but generally the l.h.s. of (A) cannot be identified with the total time-derivative of any scalar function of the potential nature. Therefore, one should look at the quantity (d/dt)(JμXμ), if at all concerned with the time behaviour of the “entropy production”. (Note that the laser gives a typical example of the violation of (A) around the unstable point, when Graham’s potential 1nP is chosen as the entropy.) In the present context, the 1.h.s. of (A) may be replaced by the average Jμ (əxμ/ət)Ψ dx, where Jμ = (1/2)Kμλ,Xλ and Xμ = (ə/əxμ)log(Ψo/ Ψ), showing that (A) is always valid.[3]μ However, what we consider here is the total derivative of P = JμXμ Ψ) dx.Google Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • H. Hasegawa
    • 1
  • S. Sawada
    • 1
  • M. Mabuchi
    • 1
  1. 1.Kyoto UniversityKyotoJapan

Personalised recommendations