1999/06/16 by Joel L. Lebowitz, Marco Lenci, Herbert Spohn · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Mechanics and Applications #Stochastic processes and statistical mechanics #cond-mat.stat-mech #math-ph #math.MP #msc:60F10 #msc:82B10 #msc:82B21
paper · pdf · doi:10.1063/1.533185
published as J. Math. Phys. 41 (2000), no. 3, 1224-1243 · 28 pages, LaTeX 2e
arxiv created 1999/06/16 · openalex publication_date 2000/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a general d-dimensional quantum system of non-interacting particles in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain Λ of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of Λ, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.