scholarly journals Entropic Uncertainty Principle, Partition Function and Holographic Principle derived from Liouville's Theorem

Physics Open ◽  
2021 ◽  
pp. 100068
Author(s):  
M.C. Parker ◽  
C. Jeynes
Keyword(s):  
Partition Function ◽  
Uncertainty Principle ◽  
Holographic Principle ◽  
Entropic Uncertainty Principle ◽  
Liouville’S Theorem

Entropic Uncertainty Principle, Partition Function and Holographic Principle derived from Liouville's Theorem

2021 ◽  
Author(s):  
M.C. Parker ◽  
C. Jeynes
Keyword(s):  
Partition Function ◽  
Uncertainty Principle ◽  
Double Helix ◽  
Logarithmic Spiral ◽  
Minkowski Spacetime ◽  
Black Hole Entropy ◽  
Previous Treatment ◽  
Holographic Principle ◽  
Entropic Uncertainty Principle ◽  
Liouville’S Theorem

Abstract An entropic version of Liouville’s theorem is defined in terms of the conjugate variables (“hyperbolic position” and “entropic momentum”) of an entropic Hamiltonian. It is used to derive the Holographic Principle as applied to holomorphic structures that represent maximum entropy configurations. The Bekenstein-Hawking expression for black hole entropy is a consequence. Based on the entropic commutator derived from Liouville’s theorem and the same entropic conjugate variables, an entropic Uncertainty Principle (in units of Boltzmann’s constant) isomorphic to the kinematic Uncertainty Principle (in units of Planck’s constant) is also derived. These formal developments underpin the previous treatment of Quantitative Geometrical Thermodynamics (QGT) which has established (entirely on geometric entropy grounds) the stability of the double-helix, the double logarithmic spiral, and the sphere. Since in the QGT formalism the Boltzmann and Planck constants are quanta of quantities orthogonal to each other in Minkowski spacetime, a solution of the Schrödinger Equation is demonstrated isomorphic to a probability term of an entropic Partition Function, where both are defined by path integrals obeying the stationary principle: this isomorphism represents an important symmetry of the formalism. The geometry of a holomorphic structure must also exhibit at least C2 symmetry.

scholarly journals Experimental investigation of the entanglement-assisted entropic uncertainty principle

2011 ◽  
Vol 7 (10) ◽  
pp. 752-756 ◽  
Author(s):  
Chuan-Feng Li ◽  
Jin-Shi Xu ◽  
Xiao-Ye Xu ◽  
Ke Li ◽  
Guang-Can Guo
Keyword(s):  
Experimental Investigation ◽  
Uncertainty Principle ◽  
Entropic Uncertainty Principle

Entanglement-assisted entropic uncertainty principle

2012 ◽  
Vol 7 (3) ◽  
pp. 259-260
Author(s):  
Kai-Min Duan ◽  
Chuan-Feng Li
Keyword(s):  
Uncertainty Principle ◽  
Entropic Uncertainty Principle
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