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Effects of Boundary Conditions on Irreversible Dynamics

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Abstract

We present a simple one-dimensional Ising-type spin system on which we define a completely asymmetric Markovian single spin-flip dynamics. We study the system at a very low, yet nonzero, temperature, and we show that for free boundary conditions the Gibbs measure is stationary for such dynamics, while introducing in a single site a \(+\) condition the stationary measure changes drastically, with macroscopical effects. We achieve this result defining an absolutely convergent series expansion of the stationary measure around the zero temperature system. Interesting combinatorial identities are involved in the proofs.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Minas Gerais, Av. António Carlos 6627, Belo Horizonte, 30161-970, Brazil

    Aldo Procacci

  2. Dipartimento di Matematica, Università di Roma“Tor Vergata”, Via della Ricerca Scientifica, 00133, Rome, Italy

    Benedetto Scoppola

  3. Dipartimento di Matematica e Fisica, Università Roma Tre, Largo San Murialdo, 1, 00146, Rome, Italy

    Elisabetta Scoppola

Authors
  1. Aldo Procacci
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  2. Benedetto Scoppola
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  3. Elisabetta Scoppola
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Corresponding author

Correspondence to Elisabetta Scoppola.

Additional information

Communicated by Christian Maes.

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Procacci, A., Scoppola, B. & Scoppola, E. Effects of Boundary Conditions on Irreversible Dynamics. Ann. Henri Poincaré 19, 443–462 (2018). https://doi.org/10.1007/s00023-017-0627-5

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  • DOI: https://doi.org/10.1007/s00023-017-0627-5

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