Is Quantum Entropy Momentum-centric?
| Main Author: | Francesco R. Ruggeri |
|---|---|
| Format: | info publication-preprint Journal |
| Terbitan: |
, 2020
|
| Subjects: | |
| Online Access: |
https://zenodo.org/record/4026031 |
Daftar Isi:
- Quantum entropy density is often written in the literature as: - [W*W] ln[W*W] - [a(p)a(p)] ln[a(p)a(p)] where W(x) is the wavefunction and a(p) its Fourier transform. Thus, the entropy is written in a symmetric way in terms of momentum and position. Recently, we suggested in (2) that quantum entropy density should be written as: -2 W dW/dx - [a(p)a(p)] ln[a(p)a(p)] which is no longer symmetric. In fact, the first term integrated over x yields 1 for any wavefunction. Thus, the entropy is really based on momentum. In this note, we investigate whether there is any reason to expect entropy should be symmetric in x and p. In classical statistical mechanics, where there may also be a spatial density due to V(x), equilibrium (described by a temperature T) is based on two particle scattering i.e on momentum considerations. In classical physics, changes in momentum due to forces is the main consideration. In quantum mechanics, we argue that interactions with a stochastic potential (which is V(x) on average) is the main driving force of “equilibrium” and that such reactions affect momentum. The spatial density is a consequence of these momentum effects and so we argue that it seems that there is no reason to consider x and p on the same footing in an expression for entropy density, even though the Heisenberg uncertainty principle also treats delta x and delta p on an equal footing. We investigate these and other issues in this note.