Abstract
The behaviour of entropy (Shannon-information) and renormalized entropy (based on theS-theorem [3]) is investigated for systems with an exponential stationary probability distribution function (1). Analytical results for the derivatives with respect to the control parameters are derived. One class of systems (3) is separated for which the renormalized entropy is a monotonously decreasing function of the control parameters.
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Nicolis, G., Prigogine, I.: Self-organization in nonequilibrium systems. New York: Wiley 1977; Moscow: Mir 1979
Haken, H.: Advanced synergetics. Berlin, Heidelberg, New York: Springer 1983; Moscow: Mir 1985
Klimontovich, Y.L.: Entropy-decrease in selforganization processes. The S-Theorem. Pis'ma Zh. Tekh. Fiz.9, 1412 (1983)
Klimontovich, Y.L.: Entropy and entropy-production in laminar and turbulent motion. Pis'ma Zh. Tekh. Fiz.10, 80 (1984)
Anishenko, V.S., Klimontovich, Y.L.: Entropy-evolution in a generator with an inert nonlinearity for the transition to chaos through period-doubling. Pis'ma Zh. Tekh. Fiz.10, 816 (1984)
Klimontovich, Y.L.: Dynamical and statistical theory of generalized Van der Pol-generators with 2k stable limit cycles (k=1,2,...). Pis'ma Zh. Tekh. Fiz.11, 21 (1985)
Klimontovich, Y.L.: Statistical Physics. Moscow: Nauka 1982; New York: Harwood Academic Press 1986
Ebeling, W., Klimontovich, Y.L.: Self-organization and turbulence in liquids. Berlin: Teubner 1984
Ebeling, W., Engel-Herbert, H., Herzel, H.: On the entropy of dissipative and turbulent structures. Ann. Phys. (Leipzig)42, 1 (1985);43, 187 (1986)
Klimontovich, Y.L.: Physica142A, 390 (1987)
Klimontovich, Y.L., Bonitz, M.: Definition of the degree of order of states in generators (self-organizing systems) with two control parameters. Pis'ma Zh. Techk. Fiz.12, 1353 (1986)
Klimontovich, Y.L., Bonitz, M.: Self-organization in systems without normal attractors. Pis'ma Zh. Tekh. Fiz.12, 1349 (1986)
Klimontovich, Y.L.: Pis'ma Zh. Tekh. Fiz.13, 175 (1987)
Klimontovich, Y.L.: Boltzmann-Gibbs entropy as measure of order in self-organizing (synergetic) systems. Springer Proceedings in Physics. Berlin, Heidelberg, New York: Springer 1987
Klimontovich, Y.L.: S-Theorem. Z. Phys. B-Condensed Matter66, 125 (1987)
Haken, H.: Information, information gain and efficiency of self-organizing systems close to instability points. Z. Phys. B-Condensed Matter61, 329 (1985)
Haken, H.: Information and information gain close to nonequilibrium phase transitions. Numerical results. Z. Phys. B-Condensed Matter62, 255 (1986)
Klimontovich, Y.L., Bonitz, M.: Definition of the degree of order in self-organization processes. Ann. Phys. (Leipzig) (in press)
Zubarev, D.N.: Nonequilibrium statistical thermodynamics. Moscow: Nauka 1971; Berlin: Akademieverlag 1976
Engel-Herbert, H.: Behaviour of entropy close to a nonequilibrium phase transition. Wissenschaftliche Zeitschrift d. Humboldt-Universität zu Berlin, Math.-Nat. R.35, 428 (1986)
Ebeling, W., Engel-Herbert, H., Herzel, H.: Thermodynamic aspects of selforganization. In: Selforganization by nonlinear irreversible processes. Ebeling W., Ulbricht H. (eds.). Berlin, Heidelberg, New York: Springer 1987
Engel-Herbert, H., Schumann, M.: Entropy decrease during excitation of sustained oscillations. Ann. Phys. (Leipzig)44, 393 (1987)
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Klimontovich, Y.L., Bonitz, M. Evolution of the entropy of stationary states in selforganization processes in the control parameter space. Z. Physik B - Condensed Matter 70, 241–249 (1988). https://doi.org/10.1007/BF01318306
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DOI: https://doi.org/10.1007/BF01318306