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arxiv: 2508.21567 · v3 · submitted 2025-08-29 · 🪐 quant-ph · cond-mat.stat-mech

Universal Precision Limits in General Open Quantum Systems

Tan Van Vu , Ryotaro Honma , Keiji Saito This is my paper

Pith reviewed 2026-05-18 20:40 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords open quantum systemsprecision limitsthermodynamic uncertaintyentropy productionasymmetry termactivity termnon-Markoviantwo-point measurements
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The pith

In open quantum systems the relative fluctuation of time-antisymmetric currents is bounded by entropy production and process asymmetry.

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

The paper derives universal precision bounds for observables in open quantum systems that couple to environments at any strength and use two-point measurements. It introduces an asymmetry term for the difference between forward and backward processes. This term adds to entropy production to limit how much time-antisymmetric currents can fluctuate relatively. General observables have their fluctuations bounded below by a generalized activity term reflecting environmental changes. Readers should care as this moves thermodynamic uncertainty relations out of the Markovian limit into more general quantum settings.

Core claim

We show that the relative fluctuation of any time-antisymmetric current is constrained not only by entropy production but also by this asymmetry. For general observables, we further prove that their relative fluctuation is always bounded from below by a generalized activity term that characterizes environmental changes. These results establish a comprehensive framework for understanding the fundamental limits of precision in a broad class of open quantum systems, beyond the traditional Markovian setting.

What carries the argument

The asymmetry term that quantifies the disparity between forward and backward processes, which works with entropy production to bound current fluctuations, and the generalized activity term that sets the lower bound for general observables by tracking environmental changes.

If this is right

  • Bounds apply to non-Markovian open quantum systems.
  • Results hold for arbitrary coupling strengths between system and environment.
  • Two-point measurements enable the definition of the necessary forward and backward processes.
  • The framework generalizes thermodynamic uncertainty relations to strongly coupled quantum regimes.

Where Pith is reading between the lines

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

  • These bounds could help in designing more precise quantum devices operating far from equilibrium.
  • The asymmetry concept might link to time-reversal properties in quantum information processing.
  • One could test the generalized activity bound in numerical simulations of quantum master equations with strong dissipation.

Load-bearing premise

Two-point measurements must capture the dynamics and forward and backward processes must be definable with a consistent asymmetry even for arbitrary couplings.

What would settle it

An explicit example or numerical simulation of an open quantum system under two-point measurements where the relative fluctuation of a time-antisymmetric current falls below the bound set by entropy production plus the asymmetry term.

Figures

Figures reproduced from arXiv: 2508.21567 by Keiji Saito, Ryotaro Honma, Tan Van Vu.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of general open quantum sys [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Numerical illustration of the main results ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

The intuition that the precision of observables is constrained by thermodynamic costs has recently been formalized through thermodynamic and kinetic uncertainty relations. While such trade-offs have been extensively studied in Markovian systems, corresponding constraints in the non-Markovian regime remain largely unexplored. In this Letter, we derive universal bounds on the precision of generic observables in open quantum systems that interact with their environments at arbitrary coupling strengths and are subjected to two-point measurements. By introducing an asymmetry term that quantifies the disparity between forward and backward processes, we show that the relative fluctuation of any time-antisymmetric current is constrained not only by entropy production but also by this asymmetry. For general observables, we further prove that their relative fluctuation is always bounded from below by a generalized activity term that characterizes environmental changes. These results establish a comprehensive framework for understanding the fundamental limits of precision in a broad class of open quantum systems, beyond the traditional Markovian setting.

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 derives universal bounds on the relative fluctuations of observables in general open quantum systems subjected to two-point measurements at arbitrary coupling strengths. It introduces an asymmetry term quantifying the disparity between forward and backward processes to bound the relative fluctuation of any time-antisymmetric current (in addition to entropy production) and proves that the relative fluctuation of general observables is bounded from below by a generalized activity term characterizing environmental changes.

Significance. If the derivations are valid, the results provide a significant extension of thermodynamic and kinetic uncertainty relations to non-Markovian regimes with strong couplings, offering a comprehensive framework for precision limits in open quantum systems. The asymmetry and generalized activity constructions are notable strengths that could enable new analyses in quantum thermodynamics.

major comments (2)
  1. [Main derivation of asymmetry term] The central claims rest on the consistent definition of forward and backward processes admitting a quantifiable asymmetry term for arbitrary system-environment couplings (see the derivation following the introduction of the asymmetry term). In non-Markovian regimes with strong coupling, persistent bath correlations can render the backward process ill-defined or non-unique without additional structure (e.g., specific initial bath states), which is load-bearing for the applicability of the bounds to generic observables.
  2. [Setup and two-point measurement protocol] The two-point measurement protocol is assumed to capture the relevant dynamics for all generic observables (see the section stating the setup for general open quantum systems). This assumption requires explicit justification or a concrete example showing how the protocol extends without weak-coupling or Markovian approximations, as it underpins both the asymmetry and generalized activity bounds.
minor comments (2)
  1. [Notation and definitions] Clarify the notation for the generalized activity term to ensure it is distinguished from standard activity measures in the literature.
  2. [Introduction] Add a brief discussion or reference to prior non-Markovian uncertainty relations to better contextualize the novelty.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work's significance and for the detailed major comments. We address each point below, providing clarifications and indicating planned revisions to the manuscript.

read point-by-point responses

  1. Referee: [Main derivation of asymmetry term] The central claims rest on the consistent definition of forward and backward processes admitting a quantifiable asymmetry term for arbitrary system-environment couplings (see the derivation following the introduction of the asymmetry term). In non-Markovian regimes with strong coupling, persistent bath correlations can render the backward process ill-defined or non-unique without additional structure (e.g., specific initial bath states), which is load-bearing for the applicability of the bounds to generic observables.

    Authors: We appreciate the referee's point on the operational definition of the backward process. In the manuscript, forward and backward processes are defined via the two-point measurement protocol on the system, with the environment initialized in a specified state (e.g., thermal equilibrium) and the full unitary dynamics of the combined system-environment Hamiltonian. The asymmetry term is then constructed from the ratio of the resulting forward and backward probability distributions of the measurement outcomes. While bath correlations are accounted for in the non-Markovian evolution, the protocol ensures the processes remain well-defined for the purpose of the bounds. We will revise the relevant section to explicitly discuss the role of the initial bath state and add a remark on why persistent correlations do not render the asymmetry ill-defined within this measurement-based framework. revision: partial

  2. Referee: [Setup and two-point measurement protocol] The two-point measurement protocol is assumed to capture the relevant dynamics for all generic observables (see the section stating the setup for general open quantum systems). This assumption requires explicit justification or a concrete example showing how the protocol extends without weak-coupling or Markovian approximations, as it underpins both the asymmetry and generalized activity bounds.

    Authors: The two-point measurement protocol is formulated without invoking weak-coupling or Markovian approximations: it consists of projective measurements on the system at initial and final times, with the intervening evolution governed by the exact system-environment unitary operator. This setup directly incorporates arbitrary couplings and non-Markovian effects through environmental correlations. To strengthen the presentation, we will add an explicit justification paragraph in the setup section, including a brief illustrative example (e.g., a two-level system coupled to a bosonic bath) demonstrating that the protocol yields the stated bounds for generic observables without those approximations. revision: yes

Circularity Check

0 steps flagged

Derivations rely on independent definitions of asymmetry and activity from forward/backward processes

full rationale

The paper introduces an asymmetry term quantifying disparity between forward and backward processes under two-point measurements and proves bounds on relative fluctuations for time-antisymmetric currents and general observables using a generalized activity term. These steps follow from standard quantum open-system dynamics and thermodynamic relations without reducing to fitted parameters, self-citations, or definitional equivalence. The central results are derived from first-principles considerations of entropy production and environmental changes rather than tautological constructions or load-bearing self-references. No equations or steps collapse the claimed bounds back to their inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The central claims rest on standard open quantum system assumptions plus the newly introduced asymmetry and activity terms; no explicit free parameters are mentioned in the abstract, but the asymmetry and activity are constructed quantities whose definitions carry the load of the bounds.

axioms (2)
  • domain assumption Open quantum systems can be described with two-point measurements that allow definition of forward and backward processes.
    Invoked in the abstract to set up the measurement protocol and asymmetry quantification.
  • domain assumption Entropy production and environmental changes can be quantified independently of the specific system-bath details.
    Required for the universal character of the bounds.
invented entities (2)
  • asymmetry term no independent evidence
    purpose: Quantifies disparity between forward and backward processes to tighten the bound on current fluctuations.
    Introduced in the abstract as a new quantity that augments entropy production.
  • generalized activity term no independent evidence
    purpose: Characterizes environmental changes to provide a lower bound on relative fluctuations of general observables.
    Introduced in the abstract as the bounding quantity for arbitrary observables.

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