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Monte Carlo simulations in the unconstrained ensemble

Ivan Latella1,*, Alessandro Campa2, Lapo Casetti3,4, Pierfrancesco Di Cintio3, J. Miguel Rubi1, and Stefano Ruffo5,6

  • 1Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
  • 2National Center for Radiation Protection and Computational Physics, Istituto Superiore di Sanità, Viale Regina Elena 299, 00161 Roma, Italy
  • 3Dipartimento di Fisica e Astronomia, Università di Firenze, and INFN, Sezione di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
  • 4INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
  • 5SISSA, via Bonomea 265 and INFN, Sezione di Trieste, 34136 Trieste, Italy
  • 6Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy

  • *ilatella@ub.edu
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Phys. Rev. E 103, L061303 – Published 21 June, 2021

DOI: https://doi.org/10.1103/PhysRevE.103.L061303

Abstract

The unconstrained ensemble describes completely open systems whose control parameters are the chemical potential, pressure, and temperature. For macroscopic systems with short-range interactions, thermodynamics prevents the simultaneous use of these intensive variables as control parameters, because they are not independent and cannot account for the system size. When the range of the interactions is comparable with the size of the system, however, these variables are not truly intensive and may become independent, so equilibrium states defined by the values of these parameters may exist. Here, we derive a Monte Carlo algorithm for the unconstrained ensemble and show that simulations can be performed using the chemical potential, pressure, and temperature as control parameters. We illustrate the algorithm by applying it to physical systems where either the system has long-range interactions or is confined by external conditions. The method opens up an avenue for the simulation of completely open systems exchanging heat, work, and matter with the environment.

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Phys. Rev. E 103, L061303– Published 21 June, 2021
  • Received 18 January 2021
  • Accepted 11 April 2021
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