Shannon entropy of wave function

Click For Summary
SUMMARY

The discussion centers on the relevance of calculating Shannon entropy for wave functions within quantum mechanics. Participants explore the concept that classical entropy is always positive, suggesting that this stems from the classical world representing a singular path in the quantum path integral framework. The idea posits that while the entropy of a complete wave function may be zero, the entropy derived from a subset of paths could yield a positive value, particularly for classical paths. This insight bridges quantum mechanics and classical thermodynamics, emphasizing the distinct nature of entropy in these domains.

PREREQUISITES
  • Understanding of quantum mechanics and wave functions
  • Familiarity with Shannon entropy and information theory
  • Knowledge of path integrals in quantum physics
  • Basic principles of classical thermodynamics
NEXT STEPS
  • Research the application of Shannon entropy in quantum mechanics
  • Study the implications of path integrals on wave function behavior
  • Explore the relationship between classical and quantum entropy
  • Investigate the mathematical proofs regarding entropy positivity in classical systems
USEFUL FOR

Physicists, quantum mechanics researchers, and students interested in the intersection of information theory and thermodynamics.

friend
Messages
1,448
Reaction score
9
Is it ever useful to find the Shannon entropy or information content of a wave function? Thanks.
 
Physics news on Phys.org
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?
 

Similar threads

Undergrad Entangled, mixed state with conditional entropy zero
  • · Replies 1 ·
Replies
1
Views
1K
High School The arrow of time (again)
  • · Replies 18 ·
Replies
18
Views
3K
Graduate Are irreversible processes absolutely irreversible, even given infinite time?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Von Neumann Entropy of a joint state
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Entropy increase in proton/proton collision?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Material Waves and Wave Functions
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad System of bosons
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Phase and group velocity for the wave function
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad The probability density of a wave function due to length contraction
  • · Replies 20 ·
Replies
20
Views
2K
Undergrad Why is a Gaussian function used to represent a wave packet?
  • · Replies 4 ·
Replies
4
Views
535