Classical Entropy from Correspondence Principle and Quantum Entropy
| Main Author: | Francesco R. Ruggeri |
|---|---|
| Format: | info publication-preprint |
| Terbitan: |
, 2020
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/4107127 |
Daftar Isi:
- The correspondence principle is used to link quantum high energy spatial density to classical spatial density C/v(x) where .5mv(x)v(x)+V(x)=E. This density is then often used to calculate Shannon’s entropy of the form - density ln(density) as in (1). In this note, we formulate classical entropy in a different manner and obtain the expression: S density= - Sum over i n(i)ln(n(i)) - (1-n(i))ln(1-n(i)) where n(i)=P(i)=Probability(i)=C/v(xi), but Integral dx C/v(x) is not force to be 1. Of course, one may not need the concept of classical entropy at all and may simply argue C/v(x) matches the high energy quantum humps. Quantum entropy still exists because the humps are caused by interference of various exp(ipx) probabilities, so there is stochasticity not present in the classical case. In a previous note, we argued that quantum entropy is -2 Integral dx Wx dW/dx + Sum over p a(p)a(-p) ln(a(p)a(-p)). The first term integrates to a constant regardless of W, but the second may be evaluated in the high energy limit which we do.