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arxiv: 2605.12993 · v1 · pith:LCRT3Q7Fnew · submitted 2026-05-13 · ✦ hep-th

Path-Integral Description of Stochastic Mechanics

Yoni BenTov This is my paper

Pith reviewed 2026-05-14 18:54 UTC · model grok-4.3

classification ✦ hep-th
keywords path integralstochastic mechanicsdiffusionWiener processdriftjumpsFeynman formalism
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The pith

The Feynman-Wiener path-integral formalism describes diffusion with drift and jumps in stochastic mechanics.

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

The paper reviews how the Feynman-Wiener path-integral approach, drawn from quantum mechanics, applies to classical stochastic processes. It establishes that this formalism captures diffusion, continuous drift, and discontinuous jumps through sums over paths. A sympathetic reader would care because it offers a single mathematical framework for handling random trajectories that traditional stochastic calculus treats separately. The review shows the formalism reproduces known results for these processes without new machinery.

Core claim

The Feynman-Wiener path-integral formalism provides a description for diffusion with drift and jumps in stochastic mechanics by extending the path-integral techniques from quantum mechanics to classical stochastic processes.

What carries the argument

The Feynman-Wiener path-integral formalism, which computes transition probabilities by summing over all possible paths including those with drift and jumps.

If this is right

  • Transition probabilities for stochastic processes follow from path sums weighted by an action-like functional.
  • Jumps appear as discontinuities in the allowed paths within the integral.
  • Drift terms modify the weighting of paths in a manner parallel to external potentials in quantum mechanics.
  • The formalism reproduces the Fokker-Planck equation in the appropriate limit.

Where Pith is reading between the lines

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

  • Numerical path-sampling algorithms could be developed to simulate jump-diffusion processes efficiently.
  • The approach may clarify links between stochastic mechanics and quantum mechanics through shared path-integral structure.
  • Extensions to systems with state-dependent jump rates would test the robustness of the formalism.

Load-bearing premise

That the standard path-integral techniques from quantum mechanics extend directly and accurately to classical stochastic processes with jumps without additional unstated corrections or limitations.

What would settle it

A direct comparison of the path-integral result for the probability distribution of a known jump-diffusion process against the exact solution of its stochastic differential equation.

Figures

Figures reproduced from arXiv: 2605.12993 by Yoni BenTov.

Figure 1
Figure 1. Figure 1: Method of sliding planks. Slide all planks to the right of [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: A stochastic process on a fixed realization of Poisson noise. [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
read the original abstract

I review the Feynman-Wiener path-integral formalism for diffusion with drift and jumps.

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.

Referee Report

0 major / 1 minor

Summary. The manuscript reviews the Feynman-Wiener path-integral formalism as a description for diffusion processes that incorporate drift and jumps, in the setting of stochastic mechanics.

Significance. As a review of an established formalism, the paper synthesizes standard path-integral techniques originally developed in quantum mechanics and applies them to classical stochastic processes. Its value lies in providing a consolidated exposition rather than new derivations; if the presentation is accurate, it may serve as a reference for researchers seeking connections between quantum path integrals and stochastic dynamics.

minor comments (1)
  1. The abstract is brief; expanding it to list the specific stochastic processes (diffusion, drift, jumps) and the target audience would improve clarity for readers.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript as a consolidated review of the Feynman-Wiener path-integral formalism for stochastic processes and for recommending acceptance. There are no major comments to address.

Circularity Check

0 steps flagged

Review paper with no internal circular derivations

full rationale

This manuscript is explicitly presented as a review of the established Feynman-Wiener path-integral formalism for diffusion, drift, and jump processes in stochastic mechanics. It draws content from prior literature without introducing new derivations, fitted parameters, or self-referential equations that reduce claims to their own inputs. The central assertion—that standard path-integral techniques extend to classical stochastic processes—relies on external established results rather than any load-bearing self-citation chain or definitional equivalence within the paper itself. No steps matching the enumerated circularity patterns are identifiable.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a review paper based solely on the abstract. No new free parameters, axioms, or invented entities are introduced by the current work; any such elements would come from the reviewed literature.

pith-pipeline@v0.9.0 · 5278 in / 960 out tokens · 54453 ms · 2026-05-14T18:54:13.448497+00:00 · methodology

discussion (0)

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Reference graph

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