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Grand canonical description of equilibrium and non-equilibrium systems using spin formalism

Author

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  • Goh, Segun
  • Woo, JunHyuk
  • Fortin, Jean-Yves
  • Choi, MooYoung

Abstract

We consider an open system in contact with a reservoir, where particles as well as energies can be exchanged between them, and present a description of the dynamics in terms of mixed (pseudo)spin and state variables. Specifically, a master equation is constructed out of the exchange rates for particles and for energies, which allows us to probe the system in the grand canonical description. In particular, employing the state resummation analysis, we obtain coupled time evolution equations for the probability distributions of the system as well as the environment. This is exemplified by a standard growth model, where the steady-state density function exhibits power-law behavior with the exponent depending on the microscopic parameters of the rate equations.

Suggested Citation

  • Goh, Segun & Woo, JunHyuk & Fortin, Jean-Yves & Choi, MooYoung, 2020. "Grand canonical description of equilibrium and non-equilibrium systems using spin formalism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    • Handle: RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120305136
    DOI: 10.1016/j.physa.2020.124983
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    References listed on IDEAS

    as
    1. Jean-Yves Fortin & Segun Goh & Chansoo Kim & MooYoung Choi, 2018. "Density distribution in two Ising systems with particle exchange," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(12), pages 1-11, December.
    2. Van den Broeck, C. & Esposito, M., 2015. "Ensemble and trajectory thermodynamics: A brief introduction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 418(C), pages 6-16.
    3. Goh, Segun & Fortin, Jean-Yves & Choi, M.Y., 2017. "Phase transitions and relaxation dynamics of Ising models exchanging particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 166-179.
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