2023/08/03 by Paul Tangney, Tangney, Paul
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Black-body radiation #Bose gas #Bose–Einstein condensate #Bose–Einstein statistics #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Einstein #Hamiltonian (control theory) #Harmonic oscillator #Ideal gas #Mathematics #Physics #Planck #Planck constant #Planck's law #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Thermal equilibrium
paper · pdf · doi:10.48550/arxiv.2308.02069
openalex publication_date 2023/08/03 · openalex created_date 2023/08/08 · openalex updated_date 2026/07/28
The microstate of any degree of freedom of any classical dynamical system can be represented by a point in its two dimensional phase space. Since infinitely precise measurements are impossible, a measurement can, at best, constrain the location of this point to a region of phase space whose area is finite. This paper explores the implications of assuming that this finite area is bounded from below. I prove that if the same lower bound applied to every degree of freedom of a sufficiently cold classical dynamical system, the distribution of the system's energy among its degrees of freedom would be a Bose-Einstein distribution.