TITLE:
Quantum Wave Probability Derive Thermodynamic Distribution
AUTHORS:
Xiaolin Li
KEYWORDS:
Quantum Wave Probability, İdentical Particle, Boltzmann Distribution, Fermi Distribution, Bose Distribution, Uniform Distribution, Boltzmann Entropy, Gibbs Paradox, Eigenstate Thermalization, ETH
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.12 No.2,
February
13,
2026
ABSTRACT: Using the concept of quantum wave probability, combined with the identity principle, we can derive the Boltzmann distribution, Fermi distribution, and Bose distribution. Different distributions correspond to different conditions. The Boltzmann condition corresponds to the Boltzmann distribution. The Fermi condition corresponds to the Fermi distribution. The Bose condition corresponds to the Bose distribution. This demonstrates that the foundation of these three statistical distributions is quantum wave probability, all originating from quantum mechanics. The Boltzmann distribution is also an independent quantum distribution and is not simply a sparse limit of the Fermi or Bose distributions. The essence of the Boltzmann distribution is a uniform distribution. The Fermi and Bose distributions are deviations from the uniform distribution. Boltzmann entropy based on the quantum wave probability can resolve the Gibbs paradox. Using this new approach, we can also derive the results of eigenstate thermalization. The equilibrium state is the state in which all eigenstates have the same temperature. We need to rethink the fundamentals of statistical mechanics.