On the Merit of a Central Limit Theorem-based Approximation in Statistical Physics

2011/11/04 by Bruno Leggio, B. Leggio, Oleg Lychkovskiy +3
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Central limit theorem #Energy (signal processing) #High-Energy Particle Collisions Research #Limit (mathematics) #Quantum #Quantum statistical mechanics #Specific heat #Statistical Mechanics and Entropy #Thermodynamic limit #cond-mat.stat-mech #quant-ph

paper · pdf · doi:10.1007/s10955-012-0442-9

published as J Stat Phys (2012) 146:1274-1287 · 12 pages, 1 figure

arxiv created 2011/11/04 · openalex publication_date 2012/02/17 · arxiv updated 2012/03/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The applicability conditions of a recently reported Central Limit Theorem-based approximation method in statistical physics are investigated and rigorously determined. The failure of this method at low and intermediate temperature is proved as well as its inadequacy to disclose quantum criticalities at fixed temperatures. Its high temperature predictions are in addition shown to coincide with those stemming from straightforward appropriate expansions up to (k_B T)^(-2). Our results are clearly illustrated by comparing the exact and approximate temperature dependence of the free energy of some exemplary physical systems.

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