1997/03/31 by Hans Henrik Rugh · 2 citations
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Statistical Mechanics and Entropy #Thermoelastic and Magnetoelastic Phenomena #chao-dyn #nlin.CD
paper · pdf · doi:10.1088/0305-4470/31/38/011
7 pages, LaTeX, uses RevTex. New sections and examples using fluctuations in the kinetic energy added
arxiv created 1998/04/16 · openalex publication_date 1998/09/25 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. We generalize the arguments in Rugh (1997 Phys. Rev. Lett. 78 772-4) and show that the energy-derivative of a micro-canonical average is itself micro-canonically observable. In particular, temperature, specific heat and higher-order derivatives of the entropy can be observed dynamically. We give perturbative, asymptotic formulae by which the canonical ensemble itself can be reconstructed from micro-canonical measurements only. Using our geometrical tools we rederive formulae by Lebowitz et al and Pearson et al , relating, for example, specific heat to fluctuations in the kinetic energy. We show that under natural assumptions on the fluctuations in the kinetic energy the micro-canonical temperature is asymptotically equivalent to the standard canonical definition using the kinetic energy.