I am not the first to match Shannon and physics

ABSTRACT Study of the linear harmonic oscillator confined in the square well with impenetrable walls is of great interest since its application for modeling parabolic quantum well semiconductor heterostructures. Fisher information and Shannon entropy, as a complexity measure for its ground and some excited energy levels are reported here.

From research gate. More from the same source:

Information Theoretic Study of the Confined Harmonic Oscillator in Position, Momentum and Phase-Space Humberto Laguna, Robin Sagar Information theories for time-dependent harmonic oscillator Jeong Ryeol Choi, Min-Soo Kim, Daeyeoul Kim, Mustapha Maamache, Salah Menouar, In Hyun Nahm

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In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal and spectral Shannon entropies. It turns out that Heisenberg's uncertainty principle can be expressed as a lower bound on the sum of these entropies. This is stronger than the usual statement of the uncertainty principle in terms of the product of standard deviations.

Not just information theoretic, it is fundamental to groups, and it is the optimum packing theory, a basis for queuing theory, built into economic logistics, market analysis, forensic accounting; any place a process counts we will find Shannon-Hartley theory. It gives the minimum number of transactions. The Huffman encoder gives the minimum spanning network for distribution. And the theory is very close to Fibonacci, which is also close to the hyperbolic, and, I think, the hyperbolic is the natural basis function for Shannon.