Shannon entropy of wave function

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The discussion centers on the utility of calculating Shannon entropy for wave functions, particularly in relation to classical and quantum mechanics. It raises the question of whether classical entropy is inherently positive due to its representation as a single path in the quantum path integral framework. The idea is proposed that if the entropy of a wave function in a path integral is zero, then the entropy of a subset of paths, specifically the classical path, could yield a positive value. This leads to a broader inquiry about the relationship between quantum and classical entropy. The conversation highlights the complexities of entropy in different physical contexts.
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Is it ever useful to find the Shannon entropy or information content of a wave function? Thanks.
 
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I'm wondering if it is possible to prove that entropy in the classical world is always positive because the classical world is just one path in the path integral and not all paths that are used in the quantum world. It occurs to me that if entropy of any wavefunction in the form of a path integral is zero, then taking the entropy of a subset of paths in the path integral would give something other than zero, maybe even always positive for just the classical path. Any thoughts?
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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