2010/04/30 by Roberto Franzosi
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Canonical ensemble #Entropy (arrow of time) #Ergodicity #Hamiltonian (control theory) #Mathematical physics #Mathematics #Microcanonical ensemble #Observable #Physics #Protein Structure and Dynamics #Quantum mechanics #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #nlin.CD
paper · pdf · doi:10.1007/s10955-011-0200-4
published as J. Stat. Phys. (2011) 143: 824-830 · 4 pages, preprint
openalex publication_date 2011/04/20 · arxiv created 2011/07/19 · arxiv updated 2015/05/18 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
We consider a generic classical many particle system described by an autonomous Hamiltonian H(x1,...,x^N+2) which, in addition, has a conserved quantity V(x1,...,x^N+2)=v, so that the Poisson bracket \H,V \ vanishes. We derive in detail the microcanonical expressions for entropy and temperature. We show that both of these quantities depend on multidimensional integrals over submanifolds given by the intersection of the constant energy hypersurfaces with those defined by V(x1,...,x^N+2)=v. We show that temperature and higher order derivatives of entropy are microcanonical observable that, under the hypothesis of ergodicity, can be calculated as time averages of suitable functions. We derive the explicit expression of the function that gives the temperature.