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  • 1
    Electronic Resource
    Electronic Resource
    Asymptotic behavior of fluctuations for the 1D Ising model in zero-temperature limit (1993)
    Springer
    Journal of statistical physics 71 (1993), S. 981-1002 
    Details
    ISSN: 1572-9613
    Keywords: Fluctuations ; 1D Ising model ; exact results ; distribution function ; zero-temperature limit ; first-order phase transition ; helix-coil transition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Fluctuation of the average spin for one-dimensional Ising spins with nearest neighbor interactions are studied. The distribution function for the average spin is calculated for a finite volume, finite temperature, and finite magnetic field. As the volume increases and the temperature diminishes at zero magnetic field, there are two limits in which the probability distribution shows quite different behaviors: in the thermodynamic limit as the volume goes to infinity for finite temperature, small deviations of the fluctuations are described by a Gaussian distribution, and in the limit as the temperature vanishes for a finite volume, the ground states are realized with probability one. The crossover between these limits is analyzed via a ratio of the correlation length to the volume. The helix-coil transition in a polypeptide is discussed as an application.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01049957
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Phase transitions in thermodynamics of a local lyapunov exponent for fully-developed chaotic systems (1992)
    Springer
    Journal of statistical physics 66 (1992), S. 727-754 
    Details
    ISSN: 1572-9613
    Keywords: Fully developed chaos ; local Lyapunov exponent ; thermodynamics ; exact solutions ; first-order phase transitions ; entropy ; coexisting states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Fluctuations in the divergence of nearby orbits are studied at a crisis point of chaos. A statistical-thermodynamic method for the description of the fluctuations is developed by using symbolic dynamics, which can explicitly write a relation between a fluctuation and reference orbit. The thermodynamics (the free energy and entropy) is exactly analyzed on a nonhyperbolic attractor of maps conjugate to the map:u→u/a for 0〈/u〈a andu→(1−u)/(1−a) fora⩽u⩽1. Te free energy has discontinuities in its slope. The entropy is directly calculated from the partition function. Then, it becomes clear that the collision of a chaotic attractor with a particular fixed point yields a singular local structure in the distribution of fluctuations. The existence of first-order phase transitions depends on the asymmetry of a map. It is shown that each of the coexisting states at the phase transition points is realized with the same probability in the thermodynamic limit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01055698
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Statistical-thermodynamic approach to a chaotic dynamical system: Exactly solvable examples (1990)
    Springer
    Journal of statistical physics 59 (1990), S. 257-297 
    Details
    ISSN: 1572-9613
    Keywords: Chaos ; natural measure ; scaling index ; symbol sequence ; one-dimensional lattice system ; thermodynamic approach ; generalized dimension ; local Lyapunov exponent ; generalized entropy ; nonhyperbolic attractor ; phase transition ; scaling law
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The static and dynamic properties of a chaotic attractor of a two-dimensional map are studied, which belongs to a particular class of piecewise continuous invertible maps. Coverings of a natural size to cover the attractor are introduced, so that the microscopic information of the attractor is written on each box composing the cover. The statistical thermodynamics of the scaling indices and the size indices of the boxes is formulated. Analytic forms of the free energy functions of the scaling indices and the size indices of the boxes are obtained for examples of a hyperbolic and a nonhyperbolic chaotic attractor. The statistical thermodynamics of local Lyapunov exponents is also studied and a relation between the thermodynamics of scaling indices and of local Lyapunov exponents is invetigated. For the nonhyperbolic example, the free energy and entropy functions of local Lyapunov exponents are obtained in analytic forms. These results display the existence of phase transitions. A phase transition is seen in the thermodynamics of scaling indices also.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01015570
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    Paper (German National Licenses)
    Fulltext
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