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  • stability
  • Springer  (2)
  • MDPI Publishing
  • 1970-1974  (2)
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  • Springer  (2)
  • MDPI Publishing
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  • 1
    Electronic Resource
    Electronic Resource
    Statistical mechanical theory of the nonlinear steady state (1974)
    Springer
    Journal of statistical physics 10 (1974), S. 139-156 
    Details
    ISSN: 1572-9613
    Keywords: Steady state ; nonlinear ; stability ; instability ; balance equation ; open system ; variational principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract By making use of perturbation techniques, we develop a theory of the non-linear steady state. We find that the linear term of a mechanical equation such as the Langevin equation is not responsible for the nonlinear terms of its expectation values at the nonequilibrium state arbitrarily far from the thermal equilibrium. The nonlinear steady state is formulated in the two cases where the microscopic conservation law exists and where it does not exist. The expressions for the expectation values of the physical quantities at the steady state are obtained as the functions of other physical quantities which are regarded as the parameters of the steady state. The stability and the instability of the steady state are discussed. A difference in the character of the instability of the steady state from that of the stationary state is discussed. It is noted that the first expansion coefficient should not exhibit an anomaly for instabilities of the steady state. The relation between the mechanical forces appearing in our approach and the corresponding thermal forces is discussed. The variational principle which is valid for the open system is developed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01009717
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  • 2
    Electronic Resource
    Electronic Resource
    Kinetic equation approach to phase transitions (1971)
    Springer
    Journal of statistical physics 3 (1971), S. 347-364 
    Details
    ISSN: 1572-9613
    Keywords: Phase transition ; kinetic theory ; Enskog-Vlasov equation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An exact mathematical discussion of the linearized Enskog-Vlasov equation is given. A criterion for the occurrence of the linear instability is related to a criterion for the occurrence of the bifurcation of the equilibrium stationary solution to the nonlinear Enskog-Vlasov equation. Mathematical results are interpreted physically in connection with phase transitions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01011389
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    Paper (German National Licenses)
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