Quantum Statistics for Distinguishable Particles

Multinomial Distribution, Quantum Statistics and Einstein-Podolsky-Rosen Like Phenomena

“…, k. The continuous random variables w i 's are of similar stochastic magnitude and the above integral (5) represents the probability of particle-arrangement if the cell probabilities were allowed to be randomly distributed in an uniform manner, specified in (3). The terminology 'arbitrary weighting' used in [4] is different in concept from that of 'random uniform prior' used here. Bose-Einstein statistics of indistinguishable particles is obtained via integration of multinomial probabilities corresponding to distinguishable particles with respect to uniform prior on .…”

“…. , n k ); see Tersoff and Bayer [4] for a similar argument leading to (5). The Maxwell-Boltzmann statistics refer to distinguishable particles.…”

Individual Particles, Properties and Quantum Statistics

“…As shown by Tersoff and Bayer [1983], one can derive quantum statistics under a hypothesis of uniformly random a priori distribution of statistical weights over all possible microstates of the system, including permuted ones. Therefore, while given FPSM an assumption of distinguishability (i.e., sensitiveness to permutations) accounts for MB statistics and one of indistinguishability (i.e., permutation invariance) for quantum statistics, it is possible to obtain BE and FD statistics for distinguishable quantum particles by denying FPSM and postulating a random a priori distribution instead.…”

Causal stochastic interpretation of Fermi—Dirac statistics in terms of distinguishable non-locally correlated particles

“…The aim of this letter is to generalize to the case of Fermi-Dirac (FD) statistics the demonstration already given by Tersoff and Bayer [3] and Kyprianidis et al [4] for Bose-Einstein (BE) statistics, i.e., to show that FD statistics can also be interpreted in terms of real subquantal motions of distinguishable particles correlated by the non-local actions-at-a-distance corresponding to a many.body quantum potential * 1 This of course (as in the BE case) implies a reevaluation of the usual assumptions about probabilities. Starting with N particles distributed among M discrete states instead of assuming that the particles will occupy each available state with an equal probability weighting w i = 1/M one introduces a random proba-1 On leave from the University of Crete, Physics Department, Heraclion, Greece.…”

“…The BE statistical distribution then immediately resuits [3] from taking the average over all possible w i without any assumption on undistinguishability. This astonishing result can be immediately justified [4] by assuming, following an assumption of Einstein himself [5] that one is not dealing with independent particles [between local stochastic collisions like in Maxwell-Boltzmann (MB) statistics] but that BE statistics "expresses indirectly a certain hypothesis of a mutual influence, which, for the moment, is of a quite mysterious nature".…”