The Boltzmann-Gibbs Distribution

Julio F. Fernández, Juan Rivero

Temur Z. Kalanov

Abstract. Modern analysis of the Boltzmann distribution on the basis of probability theory and of Gibbs quantum canonical distribution is proposed. It is shown that the Boltzmann distribution function is neither a reliable result of probability theory nor a consequence of Gibbs quantum canonical distribution. Conclusion is that the Boltzmann distribution function has no statistical and physical meaning, and the concept “Boltzmann distribution” should be abolished.

Walter Greiner, Ludwig Neise, Horst Stöcker B

Xiang Gao, Emilio Gallicchio, Adrian E. Roitberg

We show that the generalized Boltzmann distribution is the only distribution for which the Gibbs-Shannon entropy equals the thermodynamic entropy. This result means that the thermodynamic entropy and the Gibbs-Shannon entropy are not generally equal, but rather the equality holds only in the special case where a system is in equilibrium with a reservoir.