2017/04/30 by T. M. Rocha Filho, C. H. Silvestre, C.H. Silvestre +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Calculus (dental) #Classical mechanics #Complex Systems and Time Series Analysis #Epistemology #Equivalence (formal languages) #Mathematics #Monte Carlo method #Physics #Simple (philosophy) #Statistical Mechanics and Entropy #Statistical mechanics #Statistical physics #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.cnsns.2017.11.012
14 pages, 6 figures
openalex created_date 2017/04/28 · openalex publication_date 2017/11/14 · arxiv created 2017/11/17 · arxiv updated 2017/12/06 · openalex updated_date 2026/08/05
Equilibrium Statistical Mechanics is undoubtedly a cornerstone for the description of many particle systems. The common interpretation is based on ensemble theory as put forward by Gibbs, alongside the basic assumptions that different ensembles are equivalent, i.~e. the properties of the system can equally be obtained in any ensemble with the same results. However, the simplicity of the argument that provides such equivalence, mathematically grounded by the existence of Legendre transformation between the ensembles and the existence of its inverse, may break down for physical systems with long range interactions. In this paper we study the behavior of a simple toy model with a long range interaction and show from first principles, by solving numerically the mechanical equations of motion and Monte Carlo simulations, the inequivalence of ensembles, and discuss in what situations and how the Maxwell construction is applicable.