An Entropic Picture of Emergent Quantum Mechanics

Abstract

Quantum mechanics emergesà la Verlinde from a foliation of R 3 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 B . 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 R 3 . 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 from Boltzmann's constant k B .

Emergent quantum mechanics as a thermal ensemble

“…However, in the limit k B → 0 we can saturate the inequality in (32) and have ∆S = 0. The limit k B → 0 has been argued to correspond to the semiclassical limit → 0 of quantum mechanics [1]. 7 We conclude that the quantum-mechanical uncertainty principle provides the refinement (31) of the second law of thermodynamics (32), to which it becomes strictly equivalent in the semiclassical limit k B → 0.…”

“…Specifically, in [2,16] we have established a map between quantum mechanics (in the Gaussian approximation) and the classical theory of irreversible thermodynamics (in the linear regime). 1 In this latter theory [35] we have N independent thermodynamical coordinates y 1 , . .…”

“…Frequently, these takes on quantum physics can be completely recast in purely classical terms [4,29,53]. An alternative perspective, based on classical nonequilibrium thermodynamics [35], has been advocated in [1,2,16]. Beyond quantum mechanics, the relevance of nonequilibrium physics for quantum gravity and strings has been emphasised recently [18,27].…”

Two particle entanglement and its geometric duals

“…Thus it naturally led many physicists to the attempt to reformulate quantum mechanics in a geometric language, like GR. References [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] are a few such efforts towards the geometrical rewriting of quantum laws.…”

Geometric description of the Schrödinger equation in (3n+1)-dimensional configuration space

“…It is thus natural that there are numerous attempts to reformulate quantum mechanics in a more geometrical way [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”