Entropy and the central limit theorem in quantum mechanics

R.F. Streater, J. Phys., A20, 4321-4330, 1987.

ABSTRACT

We give a short proof that any infinitely divisible even representation of a Clifford algebra or a CAR algebra is quasi-free, and of Hudson's central limit theorem for fermions. We show that the entropy of any even state of the CAR, Clifford or CCR-algebra is less that or equal to the entropy of the quasi-free state with the same two-point function. The technique is to show that the entropy increases along the central limit.

REMARKS

CAR stands for canonical anticommutation relations, and CCR stands for canonical commutation relations. These are the defining relations of two C*-algebras, used to describe fermions and bosons respectively. These algebras can be extended to the cases where there are more than one type of particle; they can be written in terms of quantised fields.