The modified wave function of test particle approaching holographic screen from entropy force

TL;DR

This paper extends the concept of entropy for quantum particles near holographic screens by modifying the wave function to incorporate quantum uncertainty, linking information transfer speed to quantum entropy.

Contribution

It introduces a quantum-mechanically corrected wave function for test particles approaching holographic screens, connecting entropy, uncertainty, and information transfer.

Findings

Quantum-corrected wave function derived

Proposed probability measure for measurement on holographic screen

Derived expression for information transfer speed

Abstract

In this note we generalize entropy based on the quantum mechanical probability density distribution. Motivated by J. Munkhammar and the uncertainty of entropy we modified the origin wave function of the test particle. The corrected one acting on the quantum particle is subject to the uncertainty principle. Considering the uncertain relation, the corrected probability of the particle for measurement on holographic screen has been proposed. We also derivate the speed of information transfer described by wave function. Our quantum approach to entropy stress the information in a physical system is directly associated with its quantum mechanical entropy defined by the equality of the partition function.