2004/05/03 by F. Pennini, Pennini, F., A. Plastino +1
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Applications #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0405033
9 pages, 1 figure
arxiv created 2004/05/03 · openalex publication_date 2004/05/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the mathematical form of the information measure of Fisher's I for a Gibbs' canonical probability distribution (the most important one in statistical mechanics) incorporates important features of the intrinsic structure of classical mechanics and has a universal form in terms of "forces" and "accelerations", i.e., one that is valid for all Hamiltonian of the form T+V. If the system of differential equations associated to Hamilton's canonical equations of motion is linear, one can easily ascertain that the Fisher information per degree of freedom is proportional to the inverse temperature and to the number of these degrees. This equipartition of I is also seen to hold in a simple example involving a non-linear system of differential equations.