Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Europhysics Letters (EPL)

Why Are Independent Bosons Distributed According to Maxwell-Boltzmann Statistics?

Alexander Bach

Published Mar 1, 1991• 6 citations
Publisher

Abstract

Indistinguishable quantum particles are called distributed according to quantum Maxwell-Boltzmann statistics if the statistical operator W is Maxwell-Boltzmann symmetric, i.e. if W is a homogeneous product state. It is shown that a state is both Maxwell-Boltzmann and Bose-Einstein symmetric if and only if it is a homogeneous product state of pure states.

DOI
10.1209/0295-5075/14/5/001

Related papers

Bose-Einstein versus Maxwell-Boltzmann distributions

P. Enders, Ahornallee Senzig

The reply by Sands & Dunning-Davies [3] to my paper [1] is acknowledged concerning the distribution functions. Keywords: Maxwell-Boltzmann distribution, Bose-Einstein distribution, classical ensembles, state functions In my paper ‘Are there physical systems obeying the Maxwell-Boltzmann statistics?’[1] I have written down the well-known probabilities of the 4 possible results of one fair toss of 2 fair coins according to the Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. The two results coin 1 = head, coin 2 = tail and coin 2 = head, coin 1 = tail are counting as different in MB and as one and the same in BE and in FD. Then, I have quoted Gibbs [2], that the interchange of two © 2011 C. Roy Keys Inc. — http://redshift.vif.comApeiron, Vol. 18, No. 1, January 2011 16

•Jan 1, 2011•1 citation

On the Statistical Properties of Photons

Michele Cini

The interpretation in terms of a transition from Maxwell-Boltzmann to Bose-Einstein statistics of the effect in quantum optics of degenerate light discovered by De Martini and Di Fonzo is discussed. It is shown that the results of the experiment can be explained by using only the quantum-mechanical rule that the states of an assembly of bosons should be completely symmetrical, without mentioning in any way their statistical properties. This means that photons are indeed identical particles.

Europhysics Letters (EPL)•May 1, 1990•1 citation

Identical particles

Gennaro Auletta, Mauro Fortunato, Giorgio Parisi A

In classical physics, the question whether there are subsets of identical particles is not particularly interesting. After all, whether the particles are identical or not, we can always track each of them at any time. As we shall see, in quantum mechanics identical particles are indistinguishable because we cannot track trajectories, and this fact induces some important symmetry properties on the total wave function describing the system of particles under consideration. Generally speaking, a symmetry is an effect of an invariance, that is, the system does not change if one effects certain transformations (see Ch. 8). In this case, the system is not modified under exchange of two identical particles. Moreover, such a symmetry yields a most interesting connection between spin and statistics. After a short introduction to the significance of statistics in quantum mechanics (in Sec. 7.1), we define the permutation operator and discuss the symmetry properties of the wave function of N identical particles (Sec. 7.2). In Sec. 7.3 we show that quantum particles, differently from classical particles (that obey the Maxwell–Boltzmann statistics), may be subject to two different statistics, namely the Fermi–Dirac statistics for fermions and the Bose–Einstein statistics for bosons. In Sec. 7.4 we treat the so-called exchange interaction and, finally, in Sec. 7.5 we consider some applications of the two statistics. Statistics and quantum mechanics Identical particles are those particles whose Hamiltonian is symmetric under exchange of one particle with the other.

Cambridge University Press eBooks•Apr 16, 2009•0 citations

Indistinguishability, symmetrisation and maximum entropy

Walter T. Grandy

It is demonstrated that the distributions over single-particle states for Boltzmann, Bose-Einstein, and Fermi-Dirac statistics describing N non-interacting identical particles follow directly from the principle of maximum entropy. It is seen that the notions of indistinguishability and coarse graining are secondary, if not irrelevant. A detailed examination of the structure of the Boltzmann limit is provided.

European Journal of Physics•Apr 1, 1981•5 citations

Statistics of mesoscopic ensembles of bosons and fermions

В. А. Алексеев

Equilibrium distribution functions are obtained for boson and fermion ensembles with a limited number of particles. It is shown that the number-of-particle distribution functions in different quantum states are statistically dependent; this dependence disappears only for a large number of particles in the ensemble. The distributions are transformed into the Boltzmann distribution at a high temperature and into the Bose-Einstein and Fermi-Dirac distributions for a large number of particles in the ensemble.

Journal of Experimental and Theoretical Physics•Jun 1, 2011•4 citations

Algebraic aspects of quantum statistics

E. Celeghini, Mario Rasetti, Giuseppe Vitiello

Consistent implementation of the additivity of physical observables in second quantization uniquely establishes quantum statistics. In this scheme the usual Weyl - Heisenberg algebra induces Maxwell - Boltzmann distribution, while Bose - Einstein statistics are related to su (1,1).

Journal of Physics A Mathematical and General•Mar 21, 1997•9 citations
Indistinguishable quantum particles are called distributed according to quantum Maxwell-Boltzmann statistics if the statistical operator W is Maxwell-Boltzmann symmetric, i.e. if W is a homogeneous product state. It is shown that a state is both Maxwell-Boltzmann and Bose-Einstein symmetric if and only if it is a homogeneous product state of pure states.
The reply by Sands & Dunning-Davies [3] to my paper [1] is acknowledged concerning the distribution functions. Keywords: Maxwell-Boltzmann distribution, Bose-Einstein distribution, classical ensembles, state functions In my paper ‘Are there physical systems obeying the Maxwell-Boltzmann statistics?’[1] I have written down the well-known probabilities of the 4 possible results of one fair toss of 2 fair coins according to the Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. The two results coin 1 = head, coin 2 = tail and coin 2 = head, coin 1 = tail are counting as different in MB and as one and the same in BE and in FD. Then, I have quoted Gibbs [2], that the interchange of two © 2011 C. Roy Keys Inc. — http://redshift.vif.comApeiron, Vol. 18, No. 1, January 2011 16
In classical physics, the question whether there are subsets of identical particles is not particularly interesting. After all, whether the particles are identical or not, we can always track each of them at any time. As we shall see, in quantum mechanics identical particles are indistinguishable because we cannot track trajectories, and this fact induces some important symmetry properties on the total wave function describing the system of particles under consideration. Generally speaking, a symmetry is an effect of an invariance, that is, the system does not change if one effects certain transformations (see Ch. 8). In this case, the system is not modified under exchange of two identical particles. Moreover, such a symmetry yields a most interesting connection between spin and statistics. After a short introduction to the significance of statistics in quantum mechanics (in Sec. 7.1), we define the permutation operator and discuss the symmetry properties of the wave function of N identical particles (Sec. 7.2). In Sec. 7.3 we show that quantum particles, differently from classical particles (that obey the Maxwell–Boltzmann statistics), may be subject to two different statistics, namely the Fermi–Dirac statistics for fermions and the Bose–Einstein statistics for bosons. In Sec. 7.4 we treat the so-called exchange interaction and, finally, in Sec. 7.5 we consider some applications of the two statistics. Statistics and quantum mechanics Identical particles are those particles whose Hamiltonian is symmetric under exchange of one particle with the other.
Equilibrium distribution functions are obtained for boson and fermion ensembles with a limited number of particles. It is shown that the number-of-particle distribution functions in different quantum states are statistically dependent; this dependence disappears only for a large number of particles in the ensemble. The distributions are transformed into the Boltzmann distribution at a high temperature and into the Bose-Einstein and Fermi-Dirac distributions for a large number of particles in the ensemble.