arxiv: 2604.26856 · v1 · submitted 2026-04-29 · 🪐 quant-ph

Recognition: unknown

Fluctuations of path-dependent thermodynamic quantities in open quantum systems via two-point system-only measurements

Alessandra Colla , Andrea Smirne , Heinz-Peter Breuer , Bassano Vacchini

Authors on Pith no claims yet

Pith reviewed 2026-05-07 10:31 UTC · model grok-4.3

classification 🪐 quant-ph

keywords open quantum systemsfluctuation relationsJarzynski equalitytwo-point measurementswork and heat fluctuationspath-dependent thermodynamicsnon-Markovian dynamicsstrong coupling

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The pith

Two-point measurements performed only on the system suffice to derive exact fluctuation relations for path-dependent work and heat in open quantum systems.

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

The paper introduces a method that defines thermodynamic observables depending on the system dynamics and measures them at two times using only system degrees of freedom. This produces exact equalities for the statistics of work and heat even when the system couples arbitrarily to an environment, plus explicit correction factors that modify Jarzynski's equality. The same construction recovers known closed-system results and extends without change to strong-coupling regimes. It further shows that pure decoherence dynamics eliminates heat exchange entirely, making Jarzynski's equality hold identically regardless of coupling strength.

Core claim

By defining dynamics-dependent thermodynamic observables and performing two-point measurements solely on the system, one obtains exact equalities governing the fluctuations of path-dependent work and heat together with isolated correction terms to Jarzynski's equality, without requiring any direct access to the environment and while remaining valid for arbitrary coupling strengths.

What carries the argument

dynamics-dependent thermodynamic observables implemented through two-point measurements restricted to the system

If this is right

Exact fluctuation equalities for work and heat hold in open systems with arbitrary coupling using only system access.
Correction factors to Jarzynski's equality can be isolated and computed explicitly for given dynamics.
The framework recovers prior closed-system results and applies unchanged to strongly coupled cases.
Pure decoherence dynamics yields no heat contribution, so Jarzynski's equality for work is exact at any coupling strength.
Explicit correction factors can be calculated for a qubit undergoing phase-covariant dynamics in both weak and non-Markovian regimes.

Where Pith is reading between the lines

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

The method could reduce experimental overhead in verifying fluctuation theorems whenever environment monitoring is impractical.
It supplies a concrete route to test fluctuation relations in mesoscopic or biological quantum systems where full bath access is unavailable.
The same construction may generalize to other path-dependent quantities such as entropy production or dissipated work.
In non-Markovian regimes the size of the correction factors directly quantifies the thermodynamic cost of memory effects.

Load-bearing premise

The dynamics-dependent observables defined on the system alone must correctly reproduce the true statistics of work and heat that would be obtained if the environment were also measured.

What would settle it

A concrete comparison, on the same open quantum system, between the work and heat probability distributions extracted from system-only two-point measurements and the distributions obtained by a full system-plus-environment measurement protocol; any systematic mismatch would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.26856 by Alessandra Colla, Andrea Smirne, Bassano Vacchini, Heinz-Peter Breuer.

**Figure 1.** Figure 1: Temporal evolution of the correction factor view at source ↗

**Figure 2.** Figure 2: Temperature sensitivity of the correction factors. (a) Evolution of view at source ↗

**Figure 3.** Figure 3: Correction factors at different temperatures for the Jaynes-Cummings model. (a) Work correction factor view at source ↗

**Figure 4.** Figure 4: High-temperature dynamics of the correction fac view at source ↗

**Figure 5.** Figure 5: Correction factors at stronger couplings. (a) Evolution of view at source ↗

read the original abstract

We propose a method to evaluate general thermodynamic fluctuations in open quantum systems, based on performing a two-point measurement scheme on the system using dynamics-dependent thermodynamic observables. Our approach allows one to obtain exact equalities for fluctuations of path-dependent thermodynamic quantities such as work and heat, and to isolate correction factors to Jarzynski's equality, requiring only access to the system degrees of freedom. This framework is flexible and can be applied to the limiting case of closed systems, recovering previous, yet seemingly contradictory, results from the literature. Moreover, the formalism admits a straightforward extension to strongly coupled open quantum systems. We investigate the effect of specific dynamical classes on the fluctuation relations, and show that the pure decoherence case is particularly special, as it deterministically does not contain any heat contribution and thus constitutes a class of open system dynamics for which the Jarzynski equality for work fluctuations is identically true at any coupling strength. Finally, we look explicitly at the shape and size of the correction factors to Jarzynski's equality for a qubit undergoing phase covariant dynamics, both in the weakly-coupled regime and in the deep non-Markovian regime.

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 constructs dynamics-dependent system-only observables so two-point measurements recover exact work and heat fluctuation equalities for open systems, including strong coupling, with an exact Jarzynski result in the pure-decoherence limit.

read the letter

The central advance is a concrete way to define Hermitian operators on the system Hilbert space alone whose two-point measurement statistics match the path-dependent work and heat distributions coming from the full system-plus-bath unitary. This lets them write exact fluctuation relations and isolate the correction terms to Jarzynski’s equality without ever measuring the environment. The construction recovers the known closed-system results and extends without approximation to strong coupling, which is the part that matters for realistic devices. The pure-decoherence case is handled neatly: heat is identically zero by design, so the work relation holds exactly at any coupling strength. The qubit calculation under phase-covariant dynamics then gives explicit correction factors in both the weak-coupling and deep non-Markovian regimes, turning the abstract claim into something one can check numerically or experimentally. The framework stays inside standard quantum measurement theory and introduces no free parameters or self-referential definitions. The derivations appear to follow directly once the observables are specified by the dynamics, so the load-bearing steps look reproducible from the equations. The main soft spot is that exactness for arbitrary coupling still hinges on whether those operators can always be constructed to integrate out the bath without residual mismatch in energy accounting or trajectory statistics; the stress-test concern is therefore worth verifying in the explicit operator definitions rather than assumed. The analysis is also restricted to particular dynamical classes, so generality would be clearer with a broader proof outline or additional examples. This is aimed at people working on fluctuation theorems and quantum thermodynamics who need a system-only protocol. A reader who already knows the closed-system literature will see the extension and the special case as useful additions. It is worth sending to referees because the method is technically grounded, the special case is clean, and the qubit results make the claims falsifiable.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a framework for computing fluctuations of path-dependent thermodynamic quantities (work, heat) in open quantum systems via two-point measurements performed exclusively on the system, using specially constructed dynamics-dependent observables. The approach is claimed to deliver exact equalities for these fluctuations and explicit correction factors to Jarzynski's equality, while requiring no direct access to environmental degrees of freedom. It recovers known closed-system results, extends to strong coupling, identifies pure decoherence as a special case in which heat vanishes identically (so Jarzynski holds exactly at any coupling), and presents explicit calculations for a qubit under phase-covariant dynamics in both weak-coupling and deep non-Markovian regimes.

Significance. If the central construction is valid, the work would be significant for quantum thermodynamics: it supplies a system-only route to exact fluctuation relations that is experimentally accessible in platforms where bath monitoring is impractical, clarifies the status of Jarzynski-type equalities under open-system dynamics, and isolates concrete correction factors whose magnitude is quantified for a qubit example.

major comments (2)

[Abstract and strong-coupling extension] Abstract and the section introducing the strong-coupling extension: the claim that the formalism 'admits a straightforward extension to strongly coupled open quantum systems' and yields exact equalities for arbitrary coupling is load-bearing, yet the text supplies no explicit operator construction or derivation showing how the system-only Hermitian observables integrate out arbitrary system-bath interactions while preserving total-energy conservation and the full work/heat probability distributions.
[Pure decoherence case] Section on pure decoherence: the statement that this class 'deterministically does not contain any heat contribution' and therefore satisfies Jarzynski exactly at any coupling strength is central to the special-case analysis, but the provided text does not contain the explicit proof that the corresponding dynamics-dependent observable yields zero heat for arbitrary coupling strengths.

minor comments (1)

[Abstract] The abstract refers to 'seemingly contradictory' closed-system results in the literature; a short parenthetical citation or one-sentence reconciliation would aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major point below and will revise the manuscript to incorporate explicit derivations where they were previously only outlined.

read point-by-point responses

Referee: Abstract and the section introducing the strong-coupling extension: the claim that the formalism 'admits a straightforward extension to strongly coupled open quantum systems' and yields exact equalities for arbitrary coupling is load-bearing, yet the text supplies no explicit operator construction or derivation showing how the system-only Hermitian observables integrate out arbitrary system-bath interactions while preserving total-energy conservation and the full work/heat probability distributions.

Authors: We agree that the strong-coupling case requires a more explicit derivation. The general construction of the dynamics-dependent observables is given for open systems, but we will add a dedicated subsection that explicitly constructs the system-only Hermitian operators from the total system-bath Hamiltonian for arbitrary coupling. This will demonstrate preservation of total-energy conservation and show that the resulting two-point measurement statistics reproduce the exact work and heat distributions without reference to bath operators. revision: yes
Referee: Section on pure decoherence: the statement that this class 'deterministically does not contain any heat contribution' and therefore satisfies Jarzynski exactly at any coupling strength is central to the special-case analysis, but the provided text does not contain the explicit proof that the corresponding dynamics-dependent observable yields zero heat for arbitrary coupling strengths.

Authors: We acknowledge that the vanishing of heat in the pure-decoherence case was asserted without a complete step-by-step derivation. We will insert an explicit proof showing that, when the system-bath interaction commutes with the system Hamiltonian (pure decoherence), the dynamics-dependent heat observable constructed from system-only two-point measurements is identically zero for any coupling strength. This directly implies that the Jarzynski equality holds exactly, independent of coupling. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation grounded in measurement postulates

full rationale

The central construction defines dynamics-dependent observables on the system alone so that two-point measurement statistics reproduce the work/heat distributions obtained from the full unitary evolution. This definition is not tautological: the equalities (including Jarzynski corrections) follow from the standard two-point measurement scheme applied to those operators, combined with the unitary invariance of the total energy and the trace properties of the reduced dynamics. The pure-decoherence case is shown to yield zero heat by direct substitution into the observable definition, which is an independent structural property of the Lindblad generator rather than a fit. No self-citation is load-bearing for the exactness claim, no parameters are fitted and then relabeled as predictions, and the framework recovers known closed-system limits without redefinition. The derivation chain therefore remains self-contained against external benchmarks of quantum measurement theory.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard open-system quantum mechanics and the validity of the two-point measurement scheme with dynamics-dependent operators; no new free parameters or invented entities are introduced in the abstract.

axioms (2)

standard math Quantum mechanics and the theory of open-system dynamics (including non-Markovian and strong-coupling regimes)
Invoked to define the time evolution and the measurement operators.
domain assumption Two-point measurement scheme remains valid when observables are chosen to be dynamics-dependent
Central premise enabling system-only access to path-dependent quantities.

pith-pipeline@v0.9.0 · 5507 in / 1301 out tokens · 46623 ms · 2026-05-07T10:31:31.476728+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

100 extracted references · 6 canonical work pages · 2 internal anchors

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Fluctuations of path-dependent thermodynamic quantities in open quantum systems via two-point system-only measurements

or trajectories of the unravelings of time-local master arXiv:2604.26856v1 [quant-ph] 29 Apr 2026 2 equations [17, 18], including a recent operational scheme providing bounds (rather than equalities) of predictive power [13]. Furthermore, alternative descriptions for open systems have been formulated using quasiprobabil- ity distributions [19–21]. These a...

work page internal anchor Pith review Pith/arXiv arXiv 2026
[2]

projective measurements on the reduced system
[3]

knowledge of the reduced system, and none of the environment. With the second point, we specifically assume that one knows the dynamical map of the system at all times of the protocol (and thus its Hamiltonian) as well as its ini- tial state’s eigenbasis. As such, this framework is not intended to provide predictive power over equilibrium quantities. Itis...
[4]

distinguish between work, internal energy, and heat fluctuations
[5]

avoid the destruction of initial coherences, and thus reliably recover average quantities
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provide exact equalities that recover known results in limiting cases, in particular Jarzynski’s for closed quantum systems
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explicitly isolate correction factors to Jarzynski’s equality in open quantum systems
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assess thermodynamic fluctuations for arbitrary open systems, including strong-coupling regimes and non-Markovian dynamics, taking into account emergent contributions due to the interaction with the environment
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equilibrium counterparts

encompass different, and at times competing ap- proaches in the literature, such as [6–9, 16, 25]. The framework we propose relies on the definition of open-system thermodynamic observables, i.e., Hermitian operators acting on the system Hilbert space. These ob- servables will be used within a two-point measurement scheme (which can, for certain choices, ...
[10]

Namely, we search for an operatorOw(t)such that ⟨Ow(t)⟩t−⟨Ow(0)⟩0 =δWS(t),(32) where, compared with Eq.(7), we introduced the nota- tion⟨O⟩t = Tr{OρS(t)}

Work and heat observables An appropriate observable for work exchange should be a self-adjoint operator such that the difference of its expectation value at timetand time0gives exactly the workdoneon(orby)thesystembetweenthesetwotimes. Namely, we search for an operatorOw(t)such that ⟨Ow(t)⟩t−⟨Ow(0)⟩0 =δWS(t),(32) where, compared with Eq.(7), we introduced...
[11]

Single-time vs. two-time measurement protocols The freedom in selecting the operatorsO w(0)and Oq(0)arises from the fact that our definitions of the heat and work operators are constrained solely by the vari- ations of their expectation values. In fact, it allows us to devise qualitatively different schemes, characterized by, respectively, single-time and...
[12]

Open system work and heat equalities For any two-point observable such thatO x(0) = HS(0), and with the open system initially in a Gibbs stateρS(0) =ρG S (0)as we assume, one has that pn(0) =e−βxn(0) .(41) Then, performing the two-point measurement scheme for this observable and looking at its fluctuations using f(x) =e−βxgives ⟨e−βx⟩=ZS(t) ZS(0)Tr {e−βOx...
[13]

equi- librium counterpart

and the single impurity Anderson model [69]. Lastly, perturbative and recursive approaches are also available to find the dynamics as well as the effective Hamiltonian when an exact treatment is not possible [70–72]. B. Two-point thermodynamic fluctuations for arbitrary open systems Let us now make use of the definitions for the thermo- dynamic quantities...
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After that, the system begins to equilibrate and the magnitude of the inverse dynamical map becomes large. This, as explained in Sec. IID, leads to fast divergence of the correction factor as well as to a near-equilibrium state att f, which is outside of typical fluctuation relations scenarios. We can see the behavior of the correction factorΛw S (t), fro...

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