The Entropic Dynamics Approach to the Paradigmatic Quantum Mechanical Phenomena

Susan DiFranzo

arxiv: 1907.01730 · v1 · pith:G3EUVHB4new · submitted 2019-06-29 · 🪐 quant-ph

The Entropic Dynamics Approach to the Paradigmatic Quantum Mechanical Phenomena

Susan DiFranzo This is my paper

Pith reviewed 2026-05-25 13:26 UTC · model grok-4.3

classification 🪐 quant-ph

keywords entropic dynamicsprobability densitydiffusionentropy maximizationdouble slitharmonic oscillatorentanglementepistemic quantum mechanics

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The pith

Entropic Dynamics reproduces wave-packet spread, double-slit fringes, and entanglement by evolving a probability density under diffusion and entropy increase.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to show that the time evolution of a particle's probability density, driven by diffusion-like steps and repeated entropy maximization, generates the standard list of introductory quantum effects. A reader would care because the approach starts from logical inference with incomplete information rather than from the usual postulates, so the same mathematics might make the phenomena less mysterious. The author works through explicit cases: free expansion of a wave packet, interference in a double-slit geometry, the harmonic oscillator, and simple entangled states. In the double-slit case the calculation yields intensity minima even though probabilities are added directly, without any subtraction step. The harmonic-oscillator section links the circulation of probability current to angular momentum in a way that follows from the same entropy rule.

Core claim

A particle is described solely by a probability density whose short-time changes are diffusive; at each step the density is updated to the one that maximizes entropy subject to the constraints of the previous step. This single updating rule, applied repeatedly, produces the spreading of wave packets, the oscillatory patterns of the double-slit experiment, the stationary states of the harmonic oscillator, and the correlations of entangled pairs.

What carries the argument

The updating rule that selects, at each instant, the probability density of maximum entropy consistent with a diffusive constraint on the previous density.

If this is right

Wave-packet expansion occurs automatically once the density is allowed to diffuse while maximizing entropy at each step.
Intensity minima appear in the double-slit case even though only probabilities are added.
The probability current in the harmonic oscillator circulates in a manner that corresponds to angular momentum without separate quantization postulates.
Entangled states arise when the joint density for two particles is updated under the same entropy rule.
The same framework supplies a uniform language for discussing several textbook examples that are usually treated with different formal tools.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the update rule is universal, then any apparent conflict between probability addition and observed interference would have to be resolved inside the entropy step rather than by an extra interference postulate.
The same machinery could be applied to other systems whose textbook treatment relies on ad-hoc boundary conditions, offering a single derivation path.
Educational materials could replace separate derivations of each phenomenon with repeated application of one updating procedure.

Load-bearing premise

The assumption that diffusion plus entropy maximization by themselves are enough to produce the observed quantum patterns without any extra rules taken from standard quantum mechanics.

What would settle it

An explicit numerical integration of the entropy-maximizing update rule for the double-slit geometry that fails to place minima at the locations measured in experiment.

read the original abstract

Standard Quantum Mechanics, although successful in terms of calculating and predicting results, is inherently difficult to understand and can suffer from misinterpretation. Entropic Dynamics is an epistemic approach to quantum mechanics based on logical inference. It incorporates the probabilities that naturally arise in situations where there is missing information. The development of Entropic Dynamics involves describing a particle in terms of a probability density, and then following the time evolution of the probability density based on diffusion-like motion and maximization of entropy. Here we will apply Entropic Dynamics to several of the paradigmatic examples used in the instruction of quantum mechanics. These examples include wave packet expansion, interference, the double slit experiment, the harmonic oscillator, and entanglement. In the section on the double slit experiment, some interesting insight is gained concerning the occurrence of minima in the absence of a mechanism for destructive interference, since probabilities only add. Also, the section on the harmonic oscillator provides interesting insight into rotation and angular momentum as it pertains to the flow of probability. The last topic consists of some remarks concerning the state of education research as it pertains to quantum mechanics and the ways in which Entropic Dynamics might address them.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper re-applies the existing Entropic Dynamics framework to textbook QM examples and adds a couple of interpretive notes on the double slit and oscillator, but produces no new results or independent checks.

read the letter

This paper applies an existing Entropic Dynamics framework to standard quantum examples such as wave packet expansion, double slit interference, the harmonic oscillator, and entanglement. The central claim is that these phenomena follow from describing a particle via a probability density that evolves through diffusion-like motion and entropy maximization. What stands out is the discussion of the double slit, where minima appear even though probabilities add and there is no mechanism for destructive interference. The harmonic oscillator section also notes how the probability flow relates to rotation and angular momentum. These are the concrete points that go beyond just restating the framework. The work is solid in staying consistent with the epistemic approach and in connecting to quantum education research. It does not introduce new equations or independent tests, but it shows how the method handles these cases. The main limitation is the dependence on the prior derivations of the Schrödinger equation within Entropic Dynamics. If the constraints used in the entropy maximization steps are selected specifically to recover quantum behavior, then the reproduction of known results does not provide independent support. The abstract does not display the derivations, so the strength of the information-theoretic justification remains to be checked in the full text. This is for readers already interested in epistemic interpretations of quantum mechanics or in using such approaches for teaching. Someone looking for new predictions or resolutions to foundational problems will not find them here. I would recommend sending it for peer review. The applications are direct, the insights are modest but honest, and the paper fits within an established line of work that deserves evaluation on its own terms.

Referee Report

3 major / 2 minor

Summary. The manuscript applies the Entropic Dynamics framework—an epistemic approach based on logical inference, probability densities, diffusion-like motion, and entropy maximization—to paradigmatic quantum examples: wave-packet expansion, interference, the double-slit experiment, the harmonic oscillator, and entanglement. It claims these phenomena emerge from the time evolution of the probability density under the stated rules and offers interpretive insights, such as minima without destructive interference (probabilities add) and angular momentum as probability flow, while also commenting on quantum education research.

Significance. If the derivations are shown to rely solely on information-theoretic justifications for the diffusion current and entropy-maximization constraints without importing structures from standard quantum mechanics, the work would supply a coherent alternative perspective useful for both foundations and instruction. The multi-example application is a strength, as is the attempt to address common interpretive difficulties, but the significance is conditional on the independence of the derivations.

major comments (3)

[Double slit experiment section] Double-slit section: the assertion that interference minima arise without a mechanism for destructive interference requires an explicit statement of the entropy-maximization functional, the precise form of the diffusion current, and the auxiliary variables (e.g., drift or phase) employed; otherwise it is impossible to verify that the constraints do not already encode the phase relations of the Schrödinger equation.
[Harmonic oscillator section] Harmonic-oscillator section: the claimed insight that rotation and angular momentum appear as features of the probability flow must derive the specific current from the entropy-maximization step alone; the manuscript should show that this current is not presupposed to match the standard quantum-mechanical expression.
[Entanglement section] Entanglement remarks: the evolution of the joint probability density under diffusion plus entropy maximization must be shown to generate the observed correlations using only information-theoretic rules; the text should demonstrate that the tensor-product structure or measurement postulates are not introduced via the choice of constraints or priors.

minor comments (2)

The abstract would be clearer if it briefly indicated the form of the entropy functional or the diffusion current used in the derivations.
[Education research remarks] The education-research remarks would benefit from explicit citations to documented student misconceptions that ED is claimed to address.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and the constructive comments on the manuscript. We address each major comment below and will incorporate the requested clarifications in a revised version to strengthen the demonstration that the derivations rely on information-theoretic principles.

read point-by-point responses

Referee: [Double slit experiment section] Double-slit section: the assertion that interference minima arise without a mechanism for destructive interference requires an explicit statement of the entropy-maximization functional, the precise form of the diffusion current, and the auxiliary variables (e.g., drift or phase) employed; otherwise it is impossible to verify that the constraints do not already encode the phase relations of the Schrödinger equation.

Authors: We agree that the double-slit section would benefit from an explicit restatement of the entropy-maximization functional and the diffusion current (including any auxiliary variables) to make the independence from standard quantum mechanics fully transparent. In the revision we will insert these expressions, drawn directly from the foundational Entropic Dynamics construction, and note that they contain no phase information. revision: yes
Referee: [Harmonic oscillator section] Harmonic-oscillator section: the claimed insight that rotation and angular momentum appear as features of the probability flow must derive the specific current from the entropy-maximization step alone; the manuscript should show that this current is not presupposed to match the standard quantum-mechanical expression.

Authors: We accept the point. The revised manuscript will include an explicit derivation of the probability current for the harmonic oscillator, obtained solely from the entropy-maximization constraint at each time step, to confirm that the rotational flow is not inserted by hand to reproduce the quantum result. revision: yes
Referee: [Entanglement section] Entanglement remarks: the evolution of the joint probability density under diffusion plus entropy maximization must be shown to generate the observed correlations using only information-theoretic rules; the text should demonstrate that the tensor-product structure or measurement postulates are not introduced via the choice of constraints or priors.

Authors: We will expand the entanglement discussion to show, step by step, how the joint probability density evolves under the diffusion-plus-entropy-maximization rules and how the observed correlations arise from the information-theoretic constraints alone. The revision will explicitly note that the joint description is introduced as a single probability density on the combined configuration space, without separate tensor-product or measurement postulates. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations rely on prior ED framework

full rationale

The provided abstract and context describe ED as an epistemic inference method using probability densities evolving via diffusion-like motion and entropy maximization to reproduce QM phenomena. No equations, constraints, or self-citations are quoted that reduce any prediction to a fitted input, self-definition, or load-bearing self-citation chain. The central claim is presented as following from the stated inference rules without evidence of smuggling QM structures via ansatz or renaming. The derivation is therefore treated as self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the Entropic Dynamics premises that a particle is fully described by a probability density and that its evolution is governed by diffusion plus entropy maximization; these are domain assumptions imported from the prior framework rather than derived here.

axioms (2)

domain assumption A particle is described by a probability density over position
Stated in the abstract as the starting point of the approach.
domain assumption Time evolution is determined by diffusion-like motion together with entropy maximization
Explicitly listed in the abstract as the mechanism that generates the dynamics.

pith-pipeline@v0.9.0 · 5722 in / 1360 out tokens · 26868 ms · 2026-05-25T13:26:16.618696+00:00 · methodology

discussion (0)

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Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

development of Entropic Dynamics involves describing a particle in terms of a probability density, and then following the time evolution of the probability density based on diffusion-like motion and maximization of entropy
IndisputableMonolith/Foundation/LogicAsFunctionalEquation.lean SatisfiesLawsOfLogic echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

the transition probability P(x'|x) ... obtained by maximizing the relative entropy S[P,Q]
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean LogicNat echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

entropic time ... constructed from the evolution of the system

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