Über die Quantisierung der Entropie und die Verteilungsfunktionen von Boltzmann, Bose‐Einstein und Fermi‐Dirac

Abstract

AbstractIn a foregoing communication the concept of quantization of entropy has been introduced to derive Planck's law of black‐body radiation. In the following it is extended from photons to non‐relativistic particles. — We consider an ensemble of N particles with the total energy U which is the sum of the particle energies ε. The particles are in equilibrium with their surroundings at temperature T. In order to derive the distributions of Boltzmann, Bose‐Einstein, and Fermi‐Dirac we introduce the entropy quantum σ = ε/T which is a property of the particle itself. Again, ε and T are used from the beginning of the calculations and the distribution functions can be derived avoiding Lagrange's method for constrained maximum. Conventionally, the maximum of the entropy S for N = const, and U = const, describes the thermal equilibrium of the particle system. Instead we use the condition that the entropy quanta σ = ε/T of all particles have the same temperature T. Employing conventional particle statistics the concept of quantization of entropy leads to the same distribution functions as ordinary statistical thermodynamics, but in an easier manner.