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arxiv: 2605.19753 · v1 · pith:XJ63JLIUnew · submitted 2026-05-19 · 🪐 quant-ph

Non-Markovianity in the Adapted Caldeira-Leggett model

Luciano Manara , Andrea Smirne , Bassano Vacchini This is my paper

Pith reviewed 2026-05-20 05:57 UTC · model grok-4.3

classification 🪐 quant-ph
keywords non-MarkovianityCaldeira-Leggett modelinformation backflowopen quantum systemssystem-environment correlationsdistinguishabilityquantum decoherence
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The pith

The adapted Caldeira-Leggett model reproduces non-Markovian memory effects by tracking explicit information backflow between system and environment.

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

The paper tests whether a simplified, computationally efficient version of the Caldeira-Leggett model can still capture non-Markovian dynamics in which information flows back from the environment to the system. By following both the system and the full set of environmental oscillators, the authors measure the growth of correlations and the shifts in the environment's own state, then use distinguishability measures to quantify any revival in the reduced system's evolution. This matters because memory effects influence how quickly quantum coherence is lost and how quantum information can be preserved or recovered. The calculations show that correlation buildup depends most strongly on the system-environment coupling strength, while temperature has a larger effect on changes to the environmental state. Different quantifiers, including trace distance and the square root of the Jensen-Shannon divergence, give consistent but complementary pictures of the backflow.

Core claim

In the adapted Caldeira-Leggett model, non-Markovianity appears as a revival of distinguishability in the reduced dynamics that can be bounded from above by the buildup of system-environment correlations and by modifications to the environmental state; explicit tracking of both sets of degrees of freedom reveals that coupling strength primarily controls the correlations while temperature primarily controls the environmental changes.

What carries the argument

Distinguishability-based measure of non-Markovianity, which detects information backflow by monitoring revivals in the ability to distinguish pairs of system states or environmental states over time.

If this is right

  • Non-Markovian signatures can be traced directly to the growth of system-environment correlations whose strength scales with the coupling.
  • Temperature exerts stronger control over modifications of the environmental state than over the correlations themselves.
  • The same adapted model previously shown to reproduce decoherence and einselection also reproduces memory effects, allowing unified study of these phenomena.
  • Trace distance and square-root Jensen-Shannon divergence yield qualitatively similar but quantitatively distinct bounds on the possible information backflow.

Where Pith is reading between the lines

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

  • Parameter regimes identified here could be used to engineer baths that deliberately enhance or suppress memory effects in quantum devices.
  • The separation of coupling and temperature influences suggests experimental protocols that vary one while holding the other fixed to isolate backflow contributions.
  • The model's computational efficiency opens the possibility of extending the same tracking technique to more complex environments or to driven systems.

Load-bearing premise

The adapted model's explicit tracking of system and environment degrees of freedom faithfully reproduces the memory effects and information backflow of the full standard Caldeira-Leggett model without introducing artifacts that change the non-Markovian signatures.

What would settle it

A direct numerical comparison showing that the magnitude or timing of distinguishability revivals in the adapted model differs substantially from the corresponding quantities computed in the original Caldeira-Leggett model for identical coupling and temperature parameters would falsify the claim of reliability.

Figures

Figures reproduced from arXiv: 2605.19753 by Andrea Smirne, Bassano Vacchini, Luciano Manara.

Figure 1
Figure 1. Figure 1: Time evolution of a truncated coherent state for the free system Hamiltonian [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Trace distance D(ρ (1) S (t), ρ (1) S (t)) (left) and square root of the Jensen-Shannon divergence q J(ρ (1)(t), ρ(2)(t)) (right) as a function of time, for different values of the coupling γ , at fixed bath temperature θ = 1; the two initial open-system states are as in Eq.(26) for α = 1. the dynamics arising from two distinct initial open-system states, assuming initial global product states as in Eq.(15… view at source ↗
Figure 3
Figure 3. Figure 3: Non-Markovianity N as defined in Eq.(20) for the two initial states in Eq.(26) with the trace distance as distinguishability quantifier, as a function of the coupling γ for different values of θ (left) and as a function of the temperature θ for different values of γ (right). In [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (Left panels) Trace-distance system-environment correlations [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: System-environment correlations plus changes in the environmental state, i.e., r.h.s. of the [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
read the original abstract

In this work, we investigate the non-Markovian features of the Adapted Caldeira-Leggett model, a computationally efficient framework recently proposed to capture the essential physics of the standard Caldeira-Leggett model. While this effective model has been previously validated for decoherence and einselection, its ability to reproduce memory effects remains to be explored. By exploiting the model's capability to explicitly track both system and environment degrees of freedom, we provide a detailed characterization of non-Markovianity through the lens of information backflow. We evaluate the buildup of system-environment correlations and the corresponding modifications of the environmental state, assessing a quantitative upper bound for the revival of distinguishability in the reduced dynamics. Our results, obtained by comparing different distinguishability quantifiers such as trace distance and the square root of the Jensen-Shannon divergence, show that while correlations are primarily sensitive to coupling strength, environmental state changes are more heavily influenced by temperature. Our analysis substantiates the physical interpretation of the distinguishability-based approach to non-Markovianity, and confirms this variant of the Caldeira-Leggett model as a reliable tool for exploring the microscopic origins of different fundamental phenomena in quantum mechanics.

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 / 2 minor

Summary. The manuscript investigates non-Markovianity in the Adapted Caldeira-Leggett model, a computationally efficient variant previously validated for decoherence and einselection. By explicitly tracking system and environment degrees of freedom, the authors characterize information backflow using distinguishability measures (trace distance and square root of Jensen-Shannon divergence), analyze sensitivities of correlations to coupling strength and environmental state changes to temperature, and derive a quantitative upper bound on distinguishability revival in the reduced dynamics. They conclude that the results substantiate the physical interpretation of distinguishability-based non-Markovianity and confirm the adapted model as reliable for exploring microscopic origins of quantum phenomena.

Significance. If the adapted model reproduces the memory effects and information backflow of the standard continuous-bath Caldeira-Leggett model without discretization artifacts, the work would provide a useful tool for microscopic studies of non-Markovianity. The parameter sensitivities and quantifier comparison could clarify how correlations and environmental modifications contribute to distinguishability revivals, aiding understanding of open quantum system dynamics.

major comments (2)
  1. [Abstract and Conclusion] Abstract and concluding section: The claim that the results 'confirm this variant of the Caldeira-Leggett model as a reliable tool' for non-Markovianity is load-bearing but rests on internal analysis within the adapted framework. No side-by-side computation of non-Markovianity quantifiers (e.g., revival magnitudes or backflow measures) against the original continuous-bath model is reported, despite prior validation being limited to decoherence and einselection.
  2. [Results] Results section on upper-bound revival analysis: The quantitative upper bound for distinguishability revival is obtained from the adapted model's explicit dynamics, but without direct benchmarking to the standard Caldeira-Leggett bath, it remains unclear whether adaptation approximations alter the non-Markovian signatures that the central claim relies upon.
minor comments (2)
  1. [Methods] The notation for the square root of the Jensen-Shannon divergence should be defined explicitly in the methods to ensure reproducibility of the comparison with trace distance.
  2. [Figures] Figure captions could more clearly indicate which curves correspond to different temperature or coupling values to aid interpretation of the sensitivity claims.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments highlight important points regarding the strength of our claims about the adapted model's reliability for non-Markovianity studies. We address each major comment below, explaining our position and the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and Conclusion] Abstract and concluding section: The claim that the results 'confirm this variant of the Caldeira-Leggett model as a reliable tool' for non-Markovianity is load-bearing but rests on internal analysis within the adapted framework. No side-by-side computation of non-Markovianity quantifiers (e.g., revival magnitudes or backflow measures) against the original continuous-bath model is reported, despite prior validation being limited to decoherence and einselection.

    Authors: We acknowledge that the claim in the abstract and conclusion relies on analysis internal to the adapted model and its prior validation for decoherence and einselection. The adapted model was constructed to reproduce the essential system-environment interaction physics of the continuous-bath Caldeira-Leggett model while enabling explicit tracking of environmental degrees of freedom. Our results on information backflow, correlation buildup, and parameter sensitivities are consistent with the expected physical mechanisms of non-Markovianity. To address the concern directly, we will revise the abstract and conclusion to replace 'confirm' with 'support' and add a brief discussion of how the model's design preserves the relevant memory effects without introducing artifacts that would alter non-Markovian signatures. revision: yes

  2. Referee: [Results] Results section on upper-bound revival analysis: The quantitative upper bound for distinguishability revival is obtained from the adapted model's explicit dynamics, but without direct benchmarking to the standard Caldeira-Leggett bath, it remains unclear whether adaptation approximations alter the non-Markovian signatures that the central claim relies upon.

    Authors: The upper bound is derived analytically and numerically from the explicit joint dynamics available in the adapted model. Because the adaptation approximates the continuous bath through an effective description that matches the original model's decoherence and einselection behavior (as established previously), the non-Markovian features arising from the same interaction Hamiltonian are expected to be preserved. We will expand the results section to include additional justification based on the model's construction and the observed temperature and coupling dependencies, which align with standard expectations for information backflow. A full side-by-side numerical benchmark for revival magnitudes remains computationally intensive and is noted as future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation applies standard quantifiers to explicit model dynamics

full rationale

The paper applies standard distinguishability quantifiers (trace distance, Jensen-Shannon divergence) directly to the explicit system-environment dynamics of the adapted Caldeira-Leggett model. Non-Markovianity signatures are obtained from computed correlations and state modifications as functions of coupling and temperature. No fitted parameters are renamed as predictions, no self-definitional equations appear, and the exploration of memory effects is presented as an open question resolved by the current simulations rather than by reduction to prior self-citations. The reliability conclusion follows from the internal consistency of these computations within the model's framework.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on the previously introduced adapted Caldeira-Leggett model and standard quantum information tools; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The adapted model preserves the essential physics of the standard Caldeira-Leggett model for system-environment interactions
    Invoked when claiming the adapted version can be used to explore microscopic origins of phenomena.

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Lean theorems connected to this paper

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 unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We evaluate the buildup of system-environment correlations and the corresponding modifications of the environmental state, assessing a quantitative upper bound for the revival of distinguishability in the reduced dynamics... comparing different distinguishability quantifiers such as trace distance and the square root of the Jensen-Shannon divergence

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    the Adapted Caldeira-Leggett (ACL) model was introduced by Albrecht... its validity has been demonstrated regarding decoherence and einselection

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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