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Long-Range Order in Nonequilibrium Systems of Interacting Brownian Linear Oscillators

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Abstract

Long-range order (lro) is established with the help of a generalized Peierls argument for non-equilibrium lattice systems of one-dimensional (linear) interacting oscillators whose equation of motion (for a finite number of them) is the Smolouchowski equation for the density of a probability distribution. Interaction is mediated through the pair nearest-neighbor quadratic translation invariant potential. The initial density is Gibbsian with a potential energy satisfying the Ruelle superstability and regularity conditions.

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Authors and Affiliations

  1. Institute of Mathematics, 3 Tereshchenkivska str., Kyiv, Ukraine

    W. I. Skrypnik

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  1. W. I. Skrypnik
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Skrypnik, W.I. Long-Range Order in Nonequilibrium Systems of Interacting Brownian Linear Oscillators. Journal of Statistical Physics 111, 291–321 (2003). https://doi.org/10.1023/A:1022261125570

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  • DOI: https://doi.org/10.1023/A:1022261125570

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