Regarding the Entropy of Distinguishable Particles

Frank Hansen

A. P. Balachandran, T. R. Govindarajan, Amilcar R. de Queiroz +1 more

It has been known for some years that entanglement entropy obtained from partial trace does not provide the correct entanglement measure when applied to systems of identical particles. Several criteria have been proposed that have the drawback of being different according to whether one is dealing with fermions, bosons, or distinguishable particles. In this Letter, we give a precise and mathematically natural answer to this problem. Our approach is based on the use of the more general idea of the restriction of states to subalgebras. It leads to a novel approach to entanglement, which is suitable to be used in general quantum systems and especially in systems of identical particles. This settles some recent controversy regarding entanglement for identical particles. The prospects for applications of our criteria are wide ranging, from spin chains in condensed matter to entropy of black holes.

J. Tersoff, David Bayer

Quantum statistics can be reconciled with such classical ideas as distinguishable particles. Bose-Einstein and Fermi-Dirac statistics are derived for distinguishable particles by making an assumption regarding probabilities which is different from the traditional assumption but equally reasonable.

Benjamin W. Schumacher, Michael D. Westmoreland

Makoto Ohya, D�nes Petz

John F. Nagle

The traditional Gibbs’ calculation of the entropy of distinguishable classical particles that leads to Gibbs Paradox has been criticized recently. This criticism, if valid, would require a substantially different definition of entropy in general. However, the traditional definition of entropy works quite well in situations where the distinguishability of classical particles is taken seriously while a suggested replacement definition fails.