Is Quantum Entropy Momentum-centric?

Francesco R. Ruggeri
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...
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