pith. machine review for the scientific record. sign in

arxiv: 2605.06244 · v1 · submitted 2026-05-07 · ❄️ cond-mat.stat-mech

Recognition: unknown

Large Deviation Functions for Open Quantum Systems with a Strong Symmetry

Fei Liu, Hailong Wang, Jiayi Gu, Shanhe Su

Authors on Pith no claims yet

Pith reviewed 2026-05-08 04:51 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords large deviation functionsopen quantum systemsstrong symmetryGärtner-Ellis theoremscaled cumulant generating functiondissipative freezingnonanalyticity
0
0 comments X

The pith

Strong symmetries force block-wise Gärtner-Ellis application whose minimum recovers the true large-deviation rate function in open quantum systems.

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

In open quantum systems that possess strong symmetries, the global scaled cumulant generating function develops nonanalytic points that block direct application of the Gärtner-Ellis theorem and therefore prevent extraction of the genuine large-deviation rate function. The paper proposes that the theorem remains valid inside separate blocks of the operator space; local rate functions are obtained block by block and the global rate function is recovered simply by taking their pointwise minimum. The procedure is justified by the dissipative freezing that strong symmetries induce, which effectively decouples the dynamics into independent sectors. The scheme is illustrated analytically and on a three-spin XX model, where dephasing converts a nonanalytic point into an avoided crossing that can be tracked with degenerate perturbation theory.

Core claim

The global rate function equals the pointwise minimum of the local rate functions obtained by applying the Gärtner-Ellis theorem inside each block of the operator space; this equivalence holds because dissipative freezing partitions the dynamics according to the strong symmetry.

What carries the argument

Block decomposition of the operator space, allowing independent Gärtner-Ellis evaluation per block followed by minimization over the resulting local rate functions.

If this is right

  • Local rate functions computed inside each symmetry block can be minimized to obtain the exact global rate function.
  • Under dephasing in the three-spin XX model the nonanalytic point disappears through an avoided level crossing whose location is given by degenerate perturbation theory.
  • The block-minimization procedure applies equally to exactly solvable models and to small interacting spin systems.

Where Pith is reading between the lines

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

  • The same block-wise minimization may remove nonanalyticities caused by other degeneracies or symmetries in open quantum systems.
  • Rare-event probabilities would then be controlled by the single most probable symmetry sector rather than by the global average.
  • Numerical tests on longer chains or driven systems could check whether the avoided-crossing structure persists when the symmetry is only approximate.

Load-bearing premise

Dissipative freezing induced by the strong symmetry makes the global large-deviation behavior identical to the minimum of the independent block behaviors.

What would settle it

A numerical or analytic computation showing that the observed large-deviation rate function in a concrete strongly symmetric open system differs from the minimum of the block-wise Gärtner-Ellis rate functions would refute the proposal.

Figures

Figures reproduced from arXiv: 2605.06244 by Fei Liu, Hailong Wang, Jiayi Gu, Shanhe Su.

Figure 1
Figure 1. Figure 1: (a) The dashed and solid curves represent the local view at source ↗
Figure 2
Figure 2. Figure 2: The solid curves represent the first two largest rea view at source ↗
read the original abstract

In open quantum systems with strong symmetries, the global scaled cumulant generating function (SCGF) is generally nonanalytic, so the G\"artner-Ellis theorem cannot directly yield the genuine large-deviation rate function. To address this issue, we propose that the theorem remains valid within blocks of the systems' operator space: we first obtain local rate functions for each block via the theorem and then recover the global one by minimization. This approach is justified by the dissipative freezing phenomenon in such systems. We demonstrate the scheme in an analytical model and a three-spin model with XX interaction. In the latter, we find that the vanishing of a nonanalytic point in the global SCGF under dephasing appears as an avoided ``level'' crossing, and we quantify this behavior using a degenerate perturbation theory.

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

1 major / 2 minor

Summary. The manuscript addresses nonanalyticities in the scaled cumulant generating function (SCGF) of open quantum systems possessing strong symmetries, which prevent direct application of the Gärtner-Ellis theorem to obtain the large-deviation rate function. The authors propose that the theorem remains valid inside symmetry blocks of the operator space: local rate functions are computed block-wise via Gärtner-Ellis and the global rate function is recovered as their pointwise minimum. This construction is justified by the dissipative-freezing property. The scheme is demonstrated analytically in a solvable model and numerically on a three-spin XX chain, where dephasing converts a nonanalytic point into an avoided crossing that is quantified with degenerate perturbation theory.

Significance. If the block-wise construction holds, the work supplies a concrete route to large-deviation functions in symmetric open quantum systems where global nonanalyticities otherwise block standard methods. The analytical demonstration together with the explicit perturbation treatment of the avoided crossing in the three-spin model provides reproducible, falsifiable predictions for specific cases and illustrates how symmetry blocks decouple under dissipation.

major comments (1)
  1. [Proposal of the block-wise scheme and justification via dissipative freezing] The central claim that the global rate function equals the pointwise minimum of the block-local rate functions rests on the assertion that dissipative freezing eliminates all inter-block mixing and transient contributions. While this is verified in the analytical model and the three-spin XX example (including the perturbation analysis of the avoided crossing), no general argument is supplied that rules out corrections from block-mixing trajectories or finite-time effects outside these cases.
minor comments (2)
  1. The abstract states that the scheme is 'demonstrated analytically and on a three-spin model' but does not specify the system size or the range of parameters over which the numerical data were collected; adding this information would improve reproducibility.
  2. Notation for the local versus global SCGF and rate functions is introduced without an explicit comparison table; a short table contrasting the two would clarify the minimization step.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the careful reading of our manuscript and the constructive feedback. We respond to the single major comment below and outline the revisions we will implement.

read point-by-point responses

  1. Referee: The central claim that the global rate function equals the pointwise minimum of the block-local rate functions rests on the assertion that dissipative freezing eliminates all inter-block mixing and transient contributions. While this is verified in the analytical model and the three-spin XX example (including the perturbation analysis of the avoided crossing), no general argument is supplied that rules out corrections from block-mixing trajectories or finite-time effects outside these cases.

    Authors: We agree that the manuscript demonstrates the block-wise construction and the role of dissipative freezing explicitly in the solvable model and the three-spin XX chain (including the degenerate perturbation treatment of the avoided crossing), but does not supply a general theorem proving that dissipative freezing eliminates all inter-block mixing and transient contributions for arbitrary open quantum systems with strong symmetries. In the revised version we will add a dedicated paragraph in the Discussion section that (i) recalls the definition and established consequences of dissipative freezing for strong symmetries, (ii) states the assumptions under which the pointwise-minimum construction is expected to hold, and (iii) explicitly notes that rigorous bounds on possible corrections from block-mixing trajectories or finite-time effects remain an open question beyond the models treated here. This clarification will be added without changing the main results or the numerical/analytical demonstrations already presented. revision: yes

standing simulated objections not resolved
  • Absence of a general mathematical proof that dissipative freezing eliminates all inter-block mixing and transient contributions for arbitrary systems (the referee correctly identifies that only case-by-case verification is provided).

Circularity Check

0 steps flagged

No significant circularity; derivation applies external theorem to blocks justified by external phenomenon

full rationale

The paper's central proposal applies the Gärtner-Ellis theorem inside symmetry blocks of the operator space and recovers the global rate function as the pointwise minimum of the block-local rate functions. This is justified by invoking the dissipative freezing phenomenon rather than deriving it from the paper's equations or fitting parameters. No self-definitional loop, fitted-input-as-prediction, or load-bearing self-citation chain appears; the demonstrations in the analytical model and three-spin XX chain serve as independent checks. The argument therefore remains self-contained against external benchmarks and does not reduce the claimed result to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the dissipative freezing phenomenon as an external justification for block independence and on the standard assumptions of large-deviation theory for Markovian open systems.

axioms (1)
  • domain assumption Dissipative freezing occurs in open quantum systems with strong symmetries, allowing independent treatment of symmetry blocks.
    Invoked to justify that local rate functions can be combined by minimization without cross-block corrections.

pith-pipeline@v0.9.0 · 5434 in / 1236 out tokens · 30923 ms · 2026-05-08T04:51:49.592159+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

45 extracted references

  1. [1]

    Thus, in the operator space, L is block- diagonal: L = ⊕ Ns α =1 ⊕ Ns α ′ =1 Lαα ′

    cannot map operators within one block to an- other block [ 2]. Thus, in the operator space, L is block- diagonal: L = ⊕ Ns α =1 ⊕ Ns α ′ =1 Lαα ′ . (4) Significantly, this causes the open quantum system to have at least NS steady states, ρ (0) α for α = 1 , · · · , N s, and each residing in the diagonal blocks Bαα [ 2]. For- mally, this is expressed as Lαα...

  2. [2]

    These trajectories are composed of al- ternating deterministic pieces and random jumps of the wave functions

    can be unraveled into quantum jump tra- jectories [ 27– 30]. These trajectories are composed of al- ternating deterministic pieces and random jumps of the wave functions. Consider a quantum jump trajectory with n jumps. Let the instant and type of each jump be tk and ak, respectively, for k = 1, · · · , n . We can denote this trajectory as Xn(t) = ( a1, a...

  3. [3]

    freezing

    as follows: C[Xn(t)] = n∑ k=1 wak , (7) where the coefficient wak represents a weight assigned according to the jump type ak at the jump instant tk. In this paper, we focus on the case where the weights are simply equal to 1. Thus, the counting variable ( 7) represents the total activity [ 11]. Since the quantum jump trajectories are random in nature. Let v...

  4. [4]

    Before applying Eq

    clearly shows that the rate function in open quantum systems with strong sym- metries is generally nonconvex. Before applying Eq. ( 11), we still need to obtain the local rate functions in these diagonal blocks. Except for a few cases, such as the first model in Sec. ( IV), it is very difficult, if not impossible, to solve them directly. How- ever, the previ...

  5. [5]

    and use Eq. ( 11). In Fig. 2, we present the local and global SCGFs and rate functions under a set of parameters. To verify the data, we simulate quan- tum jump trajectories and directly extract the global rate function. We observe that these data are consistent with each other

  6. [6]

    This issue is physically relevant, as such symme- tries are subject to stringent conditions that are rarely satisfied in reality

    Effects of dephasing It is interesting to observe how the nonanalyticity of the global SCGF vanishes when strong symmetries are broken. This issue is physically relevant, as such symme- tries are subject to stringent conditions that are rarely satisfied in reality. A typical case is the presence of local dephasing [ 7, 31]. Formally, this amounts to adding ...

  7. [7]

    and the superop- erator with the counting field, Lλ () = r− (eλ − 1)σ − 1 ()σ + 1 + r+(eλ − 1)σ + 1 ()σ − 1 . (22) Because the original generator has two degenerate eigen- matrices with eigenvalue 0, the first-order corrections to 5 the eigenvalues µ ± of the tilted generator with dephasing are given by 1 2 tr L ± 1 2 √ (tr L)2 − 4 det L. (23) Here, the tra...

  8. [8]

    are de- termined only by the diagonal elements of the super- operators Ld and Lλ . These three results indicate that in the three-spin system, if the strong symmetry is slightly broken, the system’s relaxation dynamics, which is mainly determined by the Liouvillian gap, and fluctu- ations around the steady state can be fully characterized by the perturbed ...

  9. [9]

    They are in good agreement with those obtained by exact di- agonalization of the tilted generator with dephasing

    in Fig 2; see the solid symbols therein. They are in good agreement with those obtained by exact di- agonalization of the tilted generator with dephasing. V. CONCLUSION In this paper, we demonstrate that the Gärtner-Ellis theorem can be utilized to obtain the nonconvex rate function of an open quantum system with a strong symmetry. Instead of applying the...

  10. [10]

    Many-body open quantum systems.Sci- Post Phys

    Rosario Fazio, Jonathan Keeling, Leonardo Mazza, and Marco Schir/dieresis.ts1°. Many-body open quantum systems.Sci- Post Phys. Lect. Notes , page 99, 2025

    2025

  11. [11]

    A note on symmetry reductions of the lindblad equation: transport in con- strained open spin chains

    Berislav Bu?a and Toma? Prosen. A note on symmetry reductions of the lindblad equation: transport in con- strained open spin chains. New J. Phys. , 14(7):073007, July 2012

    2012

  12. [12]

    Stationary state degeneracy of open quantum systems with non-abelian symmetries

    Zh Zhang, J Tindall, J Mur-Petit, D Jaksch, and B Bu?a. Stationary state degeneracy of open quantum systems with non-abelian symmetries. J. Phys. A: Math. Theor. , 53(21):215304, May 2020

    2020

  13. [13]

    E. M. Kessler, G. Giedke, A. Imamoglu, S. F. Yelin, M. D. Lukin, and J. I. Cirac. Dissipative phase transition in a central spin system. Phys. Rev. A , 86:012116, Jul 2012

    2012

  14. [14]

    Spectral theory of liouvillians for dissi - pative phase transitions

    Fabrizio Minganti, Alberto Biella, Nicola Bartolo, and Cristiano Ciuti. Spectral theory of liouvillians for dissi - pative phase transitions. Phys. Rev. A , 98(4), October 2018

    2018

  15. [15]

    Manzano and P.I

    D. Manzano and P.I. Hurtado. Harnessing symmetry to control quantum transport. Advances in Physics , 67(1):1/dieresis.ts1C67, January 2018

    2018

  16. [16]

    Coupled activity-current fluctuations in open quan- tum systems under strong symmetries

    D Manzano, M A Mart/dieresis.ts1ªnez-Garc/dieresis.ts1ªa, and P I Hur- tado. Coupled activity-current fluctuations in open quan- tum systems under strong symmetries. New J. Phys. , 23(7):073044, July 2021

    2021

  17. [17]

    Symmetries and conservation laws in quan- tum trajectories: Dissipative freezing

    Carlos Sánchez Muñoz, Berislav Buča, Joseph Tindall, Alejandro González-Tudela, Dieter Jaksch, and Diego Porras. Symmetries and conservation laws in quan- tum trajectories: Dissipative freezing. Phys. Rev. A , 100:042113, Oct 2019

    2019

  18. [18]

    Degenerated liouvil- lians and steady-state reduced density matrices

    Juzar Thingna and Daniel Manzano. Degenerated liouvil- lians and steady-state reduced density matrices. Chaos, 31(7), 2021

    2021

  19. [19]

    On the generality of symmetry breaking and dis- sipative freezing in quantum trajectories

    Joseph Tindall, Dieter Jaksch, and Carlos S/dieresis.ts1¢nchez Mu?oz. On the generality of symmetry breaking and dis- sipative freezing in quantum trajectories. SciPost Phys. 7 Core, 6:004, 2023

    2023

  20. [20]

    Garrahan and Igor Lesanovsky

    Juan P. Garrahan and Igor Lesanovsky. Thermody- namics of quantum jump trajectories. Phys. Rev. Lett. , 104(16):160601, Apr 2010

    2010

  21. [21]

    Garrahan, and Igor Lesanovsky

    Cenap Ates, Beatriz Olmos, Juan P. Garrahan, and Igor Lesanovsky. Dynamical phases and intermittency of the dissipative quantum ising model. Phys. Rev. A , 85:043620, Apr 2012

    2012

  22. [22]

    Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state

    Igor Lesanovsky, van Merlijn Horssen, Măd ălin Guţă, and Juan P Garrahan. Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state. Phys. Rev. Lett. , 110:150401, Apr 2013

    2013

  23. [23]

    In this paper, we do not consider this case

    The exception is that there is nonzero coherent oscillator between intersubspace. In this paper, we do not consider this case

  24. [24]

    Breaking strong symmetries in dissipative quan- tum systems: Bosonic atoms coupled to a cavity

    Catalin-Mihai Halati, Ameneh Sheikhan, and Corinna Kollath. Breaking strong symmetries in dissipative quan- tum systems: Bosonic atoms coupled to a cavity. Phys. Rev. Res., 4:L012015, Feb 2022

    2022

  25. [25]

    Plenio and Peter L

    Martin B. Plenio and Peter L. Knight. The quantum- jump approach to dissipative dynamics in quantum op- tics. Rev. Mod. Phys. , 70(1):101, 1998

    1998

  26. [26]

    David E. Evans. Irreducible quantum dynamical semi- groups. Commun. Math. Phys. , 54(3):293/dieresis.ts1C297, October 1977

    1977

  27. [27]

    Albert and Liang Jiang

    Victor V. Albert and Liang Jiang. Symmetries and con- served quantities in lindblad master equations. Phys. Rev. A , 89:022118, Feb 2014

    2014

  28. [28]

    Nonequilibrium fluctuations, fluctuation the- orems, and counting statistics in quantum systems

    Massimiliano Esposito, Upendra Harbola, and Shaul Mukamel. Nonequilibrium fluctuations, fluctuation the- orems, and counting statistics in quantum systems. Rev. Mod. Phys. , 81(4):1665, 2009

    2009

  29. [29]

    Open Quantum Systems Far from Equi- librium

    Gernot Schaller. Open Quantum Systems Far from Equi- librium. Springer International Publishing, 2014

    2014

  30. [30]

    Rudge and Daniel S

    Samuel L. Rudge and Daniel S. Kosov. Counting quan- tum jumps: A summary and comparison of fixed-time and fluctuating-time statistics in electron transport. J. Chem. Phys. , 151(3):034107, July 2019

    2019

  31. [31]

    Landi, Michael J

    Gabriel T. Landi, Michael J. Kewming, Mark T. Mitchi- son, and Patrick P. Potts. Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics. PRX Quantum , 5:020201, Apr 2024

    2024

  32. [32]

    The large deviation approach to statis- tical mechanics

    Hugo Touchette. The large deviation approach to statis- tical mechanics. Phys. Rep. , 478(1-3):1–69, 2008

    2008

  33. [33]

    Edward B. Davies. Markovian master equations. Comm. Math. Phys. , 39(2):91–110, 1974

    1974

  34. [34]

    On the generators of quantum dynam- ical semigroups

    Goran Lindblad. On the generators of quantum dynam- ical semigroups. Comm. Math. Phys. , 48(2):119–130, 1976

    1976

  35. [35]

    Completely positive dy- namical semigroups of n-level systems

    Vittorio Gorini, Andrzej Kossakowski, and Ennackal Chandy Georgec Sudarshan. Completely positive dy- namical semigroups of n-level systems. J. Math. Phys. , 17(5):821–825, 1976

    1976

  36. [36]

    Carmichael, Surendra Singh, Reeta Vyas, and P

    Howard J. Carmichael, Surendra Singh, Reeta Vyas, and P. R. Rice. Photoelectron waiting times and atomic state reduction in resonance fluorescence. Phys. Rev. A , 39(3):1200–1218, February 1989

    1989

  37. [37]

    Wave- function approach to dissipative processes in quantum optics

    Jean Dalibard, Yvan Castin, and Klaus Mølmer. Wave- function approach to dissipative processes in quantum optics. Phys. Rev. Lett. , 68:580–583, Feb 1992

    1992

  38. [38]

    Monte Carlo simulation of the atomic master equation for spon- taneous emission

    Ralph Dum, Peter Zoller, and Helmut Ritsch. Monte Carlo simulation of the atomic master equation for spon- taneous emission. Phys. Rev. A , 45:4879–4887, Apr 1992

    1992

  39. [39]

    Wiseman and Gerard J

    Howard M. Wiseman and Gerard J. Milburn. Interpreta- tion of quantum jump and diffusion processes illustrated on the bloch sphere. Phys. Rev. A , 47(47):1652–1666, 1993

    1993

  40. [40]

    Dynamical symmetries and crossovers in a three-spin system with collective dissipa- tion

    S Pigeon, A Xuereb, I Lesanovsky, J P Garrahan, G De Chiara, and M Paternostro. Dynamical symmetries and crossovers in a three-spin system with collective dissipa- tion. New J. Phys. , 17(1):015010, jan 2015

    2015

  41. [41]

    L. D. Landau and E. M. Lifshits. Quantum mechanics : non-relativistic theory. Pergamon Press, New York, 1958

    1958

  42. [42]

    Andy C. Y. Li, F. Petruccione, and Jens Koch. Perturba- tive approach to markovian open quantum systems. Sci. Rep., 4(1), May 2014

    2014

  43. [43]

    Robicheaux

    Wenqi Tong and F. Robicheaux. Qualitatively altered driven dicke superradiance in extended systems due to infinitesimal perturbations. Phys. Rev. A , 110(6), De- cember 2024

    2024

  44. [44]

    Bagrets and Yuriy V

    Dmitry A. Bagrets and Yuriy V. Nazarov. Full counting statistics of charge transfer in coulomb blockade systems. Phys. Rev. B , 67:085316, February 2003

    2003

  45. [45]

    In this paper, we do not consider this case

    The exception is that there is nonzero coherent oscilla- tor between intersubspace [ 10]. In this paper, we do not consider this case