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arxiv: 2606.06259 · v1 · pith:7EJQI4GHnew · submitted 2026-06-04 · 🪐 quant-ph · cond-mat.stat-mech

Non-equilibrium thermodynamics of collapse models in the strongly non-Gaussian regime

Pedro B. Melo , Pedro V. Paraguass\'u , Simone Artini , Gabriele Lo Monaco , Sandro Donadi , Mauro Paternostro This is my paper

Pith reviewed 2026-06-28 01:16 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords collapse modelsdissipative dynamicsnon-Gaussian statesnon-equilibrium steady stateWigner entropy productionCSL modelDiósi-Penrose modelphase-space simulation
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The pith

Dissipative modifications to collapse models drive systems to non-equilibrium steady states with non-Gaussianity scaling as the cube of the dissipation parameter.

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

The paper establishes that the linear friction mechanism in the dissipative Diósi-Penrose model, extended to the CSL collapse model, maintains thermodynamic consistency in both weak and strong non-Gaussian regimes. Using Wigner phase-space analysis and a new exact pseudo-spectral method, it shows that the system reaches a non-equilibrium steady state instead of thermalizing. The asymptotic non-Gaussianity in this state scales with the third power of the dissipation strength β, and this is confirmed by positive Wigner entropy production.

Core claim

The dissipative Diósi-Penrose friction mechanism resolves the unphysical energy increase in objective collapse models by inducing a non-equilibrium steady state whose non-Gaussianity scales as the third power of the dissipation parameter. This holds across regimes when analyzed with exact numerical methods in the Wigner formalism, and the model's thermodynamic validity is verified through entropy production calculations.

What carries the argument

The linear friction mechanism of the dissipative Diósi-Penrose model extended to CSL, simulated exactly via pseudo-spectral methods in Wigner phase space to capture non-Gaussian dynamics.

If this is right

  • The system settles into a non-equilibrium steady-state rather than thermal equilibrium.
  • Asymptotic non-Gaussianity scales as the third power of the dissipation parameter β.
  • Thermodynamic consistency is confirmed by evaluating the Wigner entropy production.
  • Highly sensitive information-theoretic quantities require exact numerical methods to capture non-Gaussian tails accurately.

Where Pith is reading between the lines

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

  • This non-Gaussian scaling could provide observable signatures in precision experiments on mesoscopic quantum systems.
  • The approach might extend to other modified quantum dynamics models to check their thermodynamic properties.
  • Exact simulation methods could become standard for analyzing strong dissipation in open quantum systems.

Load-bearing premise

The novel exact pseudo-spectral simulation approach correctly captures the full non-Gaussian dynamics under strong dissipation without introducing numerical artifacts.

What would settle it

An observation that the non-Gaussianity in the steady state does not scale proportionally to the cube of the dissipation parameter β, or that the Wigner entropy production becomes negative, would falsify the claim of thermodynamic consistency.

Figures

Figures reproduced from arXiv: 2606.06259 by Gabriele Lo Monaco, Mauro Paternostro, Pedro B. Melo, Pedro V. Paraguass\'u, Sandro Donadi, Simone Artini.

Figure 1
Figure 1. Figure 1: Time evolution of the non-zero moments for a particle in a harmonic trap governed by [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Temporal evolution of the marginal PDFs. The plots display projections (upper) onto the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between the steady–state marginal PDF of the momentum as computed analytically for the free particle [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Quantitative analysis of the steady–state non [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Quantitative analysis of the evolution of non [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Time evolution of the Kullback-Leibler divergence [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Temporal evolution of the Wigner function for [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
read the original abstract

Standard objective collapse models offer a unified approach to the quantum measurement problem but predict an unphysical, indefinite increase in the energy of the system. The dissipative Di\'osi-Penrose (dDP) model resolves this heating issue by introducing a linear friction mechanism. However, this modification induces complex, non-Gaussian phase-space dynamics. We rigorously establish the thermodynamic consistency of this friction mechanism -- extended to the CSL model -- across both weakly and strongly non-Gaussian regimes. Using the Wigner phase-space formalism, we go significantly beyond the quadratic approximation and, to bypass the failure of perturbative methods under strong dissipation, introduce a novel exact pseudo-spectral simulation approach. Our analysis reveals that the system subjected to the dDP mechanism does not thermalize, but rather settles into a non-equilibrium steady-state (NESS) where the asymptotic non-Gaussianity scales as the third power of the dissipation parameter $\beta$. By evaluating the Wigner entropy production, we confirm the thermodynamic validity of the model and demonstrate that highly sensitive information-theoretic quantities require exact numerical methods to accurately capture the key non-Gaussian tails of the distribution.

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

2 major / 0 minor

Summary. The paper claims that the dissipative Diósi-Penrose (dDP) friction mechanism, extended to the CSL model, is thermodynamically consistent in both weakly and strongly non-Gaussian regimes. Using the Wigner formalism, it introduces a novel exact pseudo-spectral method to simulate the dynamics beyond the quadratic approximation, showing that the system reaches a non-equilibrium steady state (NESS) rather than thermalizing, with asymptotic non-Gaussianity scaling as β³; Wigner entropy production is evaluated to confirm validity, and the work argues that exact numerics are required for sensitive information-theoretic quantities.

Significance. If the central numerical results hold, the work provides a concrete demonstration that dissipative objective collapse models reach a NESS with a specific β³ scaling of non-Gaussianity, together with an explicit check of thermodynamic consistency via entropy production. This extends prior Gaussian-regime analyses and underscores the limitations of perturbative approaches under strong dissipation.

major comments (2)
  1. [the section introducing the pseudo-spectral simulation approach] The load-bearing claim that the pseudo-spectral solver is exact, bypasses perturbative failure, and introduces no artifacts in the non-Gaussian tails (which dominate entropy production and the β³ scaling) lacks supporting evidence. No convergence tests with respect to grid size, spectral truncation, or time-stepping, nor direct comparison against the known weak-dissipation analytic expansion, are described.
  2. [the results section on the NESS and scaling] The reported β³ scaling of asymptotic non-Gaussianity and the entropy-production results in the NESS rest entirely on the unbenchmarked numerical output; without an independent cross-check in the regime where perturbation theory remains valid, it is not possible to assess whether truncation or discretization errors affect the higher moments.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for identifying the need for explicit validation of the numerical method. The comments are well taken; we address each below and will revise the manuscript accordingly to include the requested benchmarks and cross-checks.

read point-by-point responses

  1. Referee: The load-bearing claim that the pseudo-spectral solver is exact, bypasses perturbative failure, and introduces no artifacts in the non-Gaussian tails (which dominate entropy production and the β³ scaling) lacks supporting evidence. No convergence tests with respect to grid size, spectral truncation, or time-stepping, nor direct comparison against the known weak-dissipation analytic expansion, are described.

    Authors: We agree that the manuscript as submitted does not present explicit convergence tests or a direct comparison to the weak-dissipation analytic expansion. In the revised version we will add a dedicated subsection reporting convergence with respect to grid size, spectral truncation, and time-step size, together with a quantitative comparison of the numerical non-Gaussianity and entropy production against the known perturbative expansion for small β. These additions will supply the requested evidence that discretization and truncation errors do not affect the reported tails or scaling. revision: yes

  2. Referee: The reported β³ scaling of asymptotic non-Gaussianity and the entropy-production results in the NESS rest entirely on the unbenchmarked numerical output; without an independent cross-check in the regime where perturbation theory remains valid, it is not possible to assess whether truncation or discretization errors affect the higher moments.

    Authors: We concur that an independent cross-check in the perturbative regime is required to validate the numerics. The revised manuscript will include a direct comparison, in the weak-dissipation limit, between the pseudo-spectral results and the analytic expansion for both the asymptotic non-Gaussianity and the Wigner entropy production. Agreement in this regime will confirm that the β³ scaling observed at stronger dissipation is not an artifact of the discretization. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper's central claims rest on the standard Wigner phase-space formalism (not redefined here) and a newly introduced pseudo-spectral numerical solver whose validity is asserted via exactness claims rather than any reduction to fitted parameters or prior self-citations. No equations or results are shown to equal their inputs by construction, no uniqueness theorems are imported from the authors' own prior work, and entropy-production evaluation follows directly from established definitions without self-referential fitting. The analysis therefore remains independent of the target results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Ledger constructed from abstract only; full paper may contain additional model parameters or assumptions in the CSL extension and numerical implementation.

axioms (1)
  • domain assumption The Wigner phase-space formalism provides an accurate representation of the quantum dynamics for the dissipative collapse model in the non-Gaussian regime.
    Invoked to analyze dynamics beyond the quadratic approximation.

pith-pipeline@v0.9.1-grok · 5744 in / 1291 out tokens · 49955 ms · 2026-06-28T01:16:00.229898+00:00 · methodology

discussion (0)

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Reference graph

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