An entropic picture of emergent quantum mechanics

TL;DR

This paper proposes a thermodynamic and entropic framework for emergent quantum mechanics, deriving quantum phenomena from holographic screens and entropy exchange, connecting classical thermodynamics with quantum theory.

Contribution

It introduces an entropic perspective on emergent quantum mechanics, deriving quantum behavior from holographic thermodynamics and linking Planck's constant to Boltzmann's constant.

Findings

Quantum mechanics emerges from holographic entropy exchange.

Planck's constant h is formally derived from Boltzmann's constant k.

Thermodynamics on holographic screens reproduces quantum phenomena.

Abstract

Quantum mechanics emerges a la Verlinde from a foliation of space by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on space. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant h from Boltzmann's constant k.