Pith. sign in

REVIEW 1 major objections 5 minor 1 cited by

Precision bounds for any current in coherent nanoscale transport

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Thermodynamic, kinetic, and thermokinetic uncertainty relations are derived for arbitrary currents in coherent transport, remaining valid far from equilibrium and in superconducting hybrid structures.

T0 review reviewed 2026-07-08 challenge →

load-bearing objection Solid extension of TUR/KUR to arbitrary currents in coherent transport; the involution existence is assumed but the framework is constructive and the examples land. the 1 major comments →

arxiv 2607.06190 v1 pith:7KLKMV3O submitted 2026-07-07 cond-mat.mes-hall cond-mat.stat-mech

Uncertainty relations for arbitrary currents in coherent transport

Ludovico Tesser , Janine Splettstoesser This is my paper
classification cond-mat.mes-hall cond-mat.stat-mech
keywords arbitrarycoherentcurrentsequilibriumrelationstransportuncertaintyvalid
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper proves that thermodynamic and kinetic uncertainty relations — which bound how precise a transported current can be relative to its fluctuations — hold for arbitrary transported quantities in coherent, strongly coupled, linear systems out of equilibrium, not just for particle currents as previously shown. The authors derive three bounds (thermodynamic, kinetic, and a unified thermokinetic relation) starting from the probability distribution of individual scattering events. The key mechanism is a two-step application of the Cauchy-Schwarz inequality: first at the level of single-scattering-event statistics over a symmetrized probability distribution built from fluctuation theorems, then again at the level of energy-resolved integrals over those events. The thermodynamic bound uses the forward-backward stochastic entropy (a quantity that satisfies a fluctuation theorem by construction and coincides with thermodynamic entropy production in time-reversal symmetric systems), while the kinetic bound uses a stochastic activity variable counting events where the transported quantity changes. Crucially, both bounds naturally incorporate higher-order fluctuations of entropy and activity, which become significant far from equilibrium and at strong coupling. This allows the bounds to remain valid where classical (near-equilibrium or weak-coupling) limits are violated — including in superconducting hybrid structures where Andreev reflections transfer charge without entropy change, causing previous particle-current-specific bounds to fail for charge-current precision. The authors demonstrate the bounds in normal-metal and normal-superconducting junctions, showing they are tighter and more general than existing formulations.

Core claim

The central result is that the Cauchy-Schwarz inequality, applied first to the symmetrized probability distribution of individual scattering events and then to the energy-resolved integral over those events, yields uncertainty relations for any antisymmetric transported quantity. The thermodynamic bound has cost C = integral of E[tanh(sigma/2)] / (1 - E[tanh(sigma/2)]), the kinetic bound has cost A = integral of E[a] / (1 - E[a]), and a unified thermokinetic bound combines both. These bounds reduce to the classical TUR and KUR near equilibrium and at weak coupling respectively, but remain valid far from equilibrium and in superconducting structures where all prior bounds — which were proven只

What carries the argument

1) Forward-backward stochastic entropy sigma = log[p(omega)/p(omega^double_dagger)], which satisfies a fluctuation theorem by construction and coincides with thermodynamic entropy production in time-reversal symmetric systems. 2) A symmetrized probability distribution p_+ = (p(omega) + p(omega^double_dagger))/2 on which Cauchy-Schwarz is applied. 3) A stochastic activity variable a(omega) = 1 - delta_{q(omega),0} counting events where the transported quantity changes. 4) The factorization of average current and zero-frequency noise into energy-resolved integrals over single-scattering-event statistics (Eq. 2), which connects the single-event Cauchy-Schwarz bounds to macroscopic transport.

Load-bearing premise

The entire derivation requires that the average current and zero-frequency noise factorize into energy-resolved integrals over single-scattering-event statistics. This factorization is valid only for noninteracting (or mean-field) systems where the Levitov-Lesovik full counting statistics applies. If particle-particle interactions cannot be neglected, the probability distribution over scattering events is not well-defined in this form and the Cauchy-Schwarz argument collapses

What would settle it

A concrete counterexample would be a coherent, strongly coupled, linear system out of equilibrium where the precision of some antisymmetric transported quantity exceeds the bound C (or A, or the thermokinetic bound) while Eq. (2) remains valid. More realistically, the bounds could be tested numerically or experimentally in normal-superconducting junctions with energy-dependent transmissions: if any observable's precision-to-noise ratio exceeds the integral bound while the factorization holds, the Cauchy-Schwarz step would be contradicted. The authors' own numerical sampling of random observals

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • The bounds apply to any antisymmetric transported quantity — charge, energy, quasiparticle number, or arbitrary observables — removing the restriction to particle currents that limited all prior coherent-transport uncertainty relations.
  • In superconducting hybrid structures, the bounds correctly constrain charge-current precision even though Andreev reflections transfer charge without entropy production, a scenario where previous bounds were violated.
  • Far from equilibrium, higher-order moments of entropy production and activity provide positive corrections to the cost, meaning coherent conductors can exceed classical precision limits without violating any bound.
  • The unified thermokinetic bound interpolates between the thermodynamic and kinetic costs, and its tightness depends on how restrictively one defines the class of events contributing to the activity.
  • The framework extends to time-reversal symmetry breaking (e.g., magnetic fields), where the forward-backward entropy differs from thermodynamic entropy production but the mathematical bound remains valid.

Where Pith is reading between the lines

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

  • The factorization requirement (Eq. 2) means these bounds are fundamentally limited to noninteracting or mean-field systems. Extending to genuinely interacting systems would require replacing the single-scattering-event probability distribution with a many-body counting statistics framework, where the Cauchy-Schwarz strategy may not directly apply.
  • The connection between the kinetic activity defined here and quantum Fisher information (noted in related work by the authors) suggests that the thermokinetic bound might be interpretable as a quantum Cramér-Rao bound for a specific measurement channel, which would connect precision limits to parameter estimation theory.
  • The dependence of the thermokinetic bound's tightness on the choice of involution (global vs. local reversal) suggests an optimization principle: the tightest bound for a given observable is obtained by choosing the involution that maximizes the number of null-activity events, which could be formulated as a variational problem.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 5 minor

Summary. This Letter derives thermodynamic, kinetic, and thermokinetic uncertainty relations (TUR, KUR, TKUR) for arbitrary transported quantities in coherent, strongly-coupled, linear systems out of equilibrium. The central results are Eqs. (8), (13), and (17). The approach starts from the Levitov-Lesovik full counting statistics framework [Eq. (2)], defines a forward-backward stochastic entropy via an involution on the sample space [Eq. (4a)], and applies Cauchy-Schwarz to obtain bounds on the precision of any current. The near-equilibrium [Eqs. (9, 14)] and weak-coupling limits recover known classical results. The framework is illustrated in normal-metal (NN) and normal-superconducting (NS) hybrid setups, demonstrating that the bounds remain valid far from equilibrium and in superconducting structures where previous particle-current-specific bounds are violated.

Significance. The main contribution is the generalization of uncertainty relations from particle currents to arbitrary transported quantities (charge, energy, quasiparticle currents) in coherent transport. The derivation is parameter-free: the bounds follow directly from Cauchy-Schwarz applied to the fluctuation theorem [Eq. (4a)] and the activity definition [Eq. (10)], with no fitted parameters. The NS setup example [Fig. 2] provides a concrete and physically relevant demonstration where existing bounds fail and the new ones hold. The random-observable sampling in Fig. 2(c,d) provides falsifiable numerical evidence for the bounds across a range of parameters. The framework correctly identifies that higher-order fluctuations of entropy production and activity enter the cost far from equilibrium, explaining apparent violations of classical bounds.

major comments (1)
  1. The involution existence and its compatibility with the FCS probability distribution are assumed without proof. The TUR [Eq. (8)] and TKUR [Eq. (17)] both rely on the forward-backward entropy defined via an involution satisfying q(ω†) = -q(ω) [Eq. (3)]. The paper states 'we first consider an involution on the sample space' without proving that such an involution exists for arbitrary transported quantities Q in arbitrary multi-terminal or superconducting setups. For the NN example, the global reversal (n1,...,nr)† = (-n1,...,-nr) works for particle number, but for a general observable q (e.g., energy current in a multi-terminal setup with Andreev processes), it is not obvious that an involution exists on the FCS sample space that simultaneously (i) is an involution, (ii) makes q antisymmetric, and (iii) yields a σ̃ that coincides with thermodynamic entropy production in the time-reversal-
minor comments (5)
  1. Eq. (2): the notation h is introduced without explicit definition; it appears to be a measure factor (possibly related to the density of states or the quantum of conductance), but this should be stated.
  2. The transition from Eq. (6a) to Eq. (6b) involves mapping expectations from p+ back to p; the step E+[q tanh(σ̃/2)]² = E[q]² should be made more explicit for the reader.
  3. Fig. 1(b,c,e,f): the y-axis labels show multiple quantities (P_N, P_E, costs); a legend or clearer labeling would improve readability.
  4. The comparison with Eq. (19) is dropped after Fig. 1(f) because it does not bound P_E; it would be helpful to note that Eq. (19) was derived for particle currents (tunneling events only).
  5. Conclusions: the statement about time-reversal symmetry breaking could benefit from a brief clarification that the bound [Eq. (7)] remains mathematically valid but the physical interpretation of σ̃ changes.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for a careful reading and a constructive report. The referee correctly identifies the central contributions of our Letter: the generalization of uncertainty relations to arbitrary transported quantities in coherent transport, the parameter-free derivation from Cauchy-Schwarz applied to the fluctuation theorem, and the demonstration in normal and superconducting hybrid structures. The one substantive concern raised—regarding the existence and compatibility of the involution for general observables in multi-terminal and superconducting setups—is well-taken. We agree that the manuscript should state more explicitly the conditions under which the involution exists and how it is constructed in the examples considered, and we will revise accordingly.

read point-by-point responses

  1. Referee: The involution existence and its compatibility with the FCS probability distribution are assumed without proof. The TUR [Eq. (8)] and TKUR [Eq. (17)] both rely on the forward-backward entropy defined via an involution satisfying q(ω†) = -q(ω) [Eq. (3)]. The paper states 'we first consider an involution on the sample space' without proving that such an involution exists for arbitrary transported quantities Q in arbitrary multi-terminal or superconducting setups. For the NN example, the global reversal (n1,...,nr)† = (-n1,...,-nr) works for particle number, but for a general observable q (e.g., energy current in a multi-terminal setup with Andreev processes), it is not obvious that an involution exists on the FCS sample space that simultaneously (i) is an involution, (ii) makes q antisymmetric, and (iii) yields a σ̃ that coincides with thermodynamic entropy production in the time-reversal-

    Authors: The referee raises a valid point: the manuscript does not explicitly state the conditions under which the involution exists or how it is constructed in the examples. We will revise the manuscript to clarify this. To address the substance of the comment, we note the following. The involution we use in both the NN and NS examples is the time-reversal involution on the FCS sample space, which exchanges the initial and final states of each scattering event. This involution is well-defined for the Levitov-Lesovik FCS framework: each scattering event ω is characterized by the set of transferred particle numbers (n_1, ..., n_r) across terminals, and the involution maps (n_1, ..., n_r) → (-n_1, ..., -n_r). This map is always an involution regardless of the observable q. The additional requirement is that q be antisymmetric under this map [Eq. (3)]. For particle number, charge, and energy currents in the NN setup, this antisymmetry holds because the transferred quantity changes sign when all particle numbers are reversed. In the NS setup, the BTK scattering amplitudes define the FCS distribution, and the same global reversal involution applies; the quasiparticle number, charge, and energy transferred all change sign under this map, so antisymmetry is satisfied. The key point is that the involution is defined on the sample space Ω (independent of q), and the antisymmetry condition [Eq. (3)] is a property of the observable q with respect to that involution—not a requirement that the involution be constructed separately for each q. For observables that are odd under time reversal (which includes all standard currents: particle, charge, energy, and quasiparticle currents), the global reversal involution satisfies all three conditions (i)-(iii) simultaneously. We agree that the paper revision: partial

Circularity Check

1 steps flagged

No significant circularity; derivation is self-contained via Cauchy-Schwarz and fluctuation-theorem identities, with minor self-citations providing context rather than load-bearing support.

specific steps
  1. self citation load bearing [Eq. (4a) and surrounding text]
    "the forward-backward stochastic entropy ˜σ[28, 31] and the symmetrized probability distribution p+ as ˜σ(ω) := log p(ω)/p(ω‡)"

    The forward-backward entropy ˜σ is defined by Eq. (4a) as a log-ratio of p(ω)/p(ω‡). The paper states 'By definition, ˜σ fulfills a fluctuation theorem [Eq. (4a)]' and then uses this fluctuation theorem in the Cauchy-Schwarz derivation of the TUR. This is not circular in the problematic sense: the fluctuation theorem is a tautological consequence of the definition of ˜σ, not an independent assumption. The Cauchy-Schwarz inequality [Eq. (6)] is then applied to derive the bound [Eq. (8)], which is a genuine mathematical consequence. The self-citations [28, 31] (Ref. 28 is the first author's thesis) provide the origin of the ˜σ concept but the definition is self-contained in the paper. This is a minor self-citation that is not load-bearing for the mathematical derivation.

full rationale

The central derivation chain is mathematically self-contained. The TUR [Eq. (8)] follows from Cauchy-Schwarz [Eq. (6)] applied to the identity in Eq. (5), which is itself a consequence of the definition of ˜σ in Eq. (4a). The KUR [Eq. (13)] follows from Cauchy-Schwarz [Eq. (11)] applied to the activity definition [Eq. (10)]. The TKUR [Eq. (17)] combines both. No step reduces to its inputs by construction in a way that would make the bounds trivially equivalent to fitted parameters or definitions. The bounds are inequalities, not equalities, and the right-hand sides (costs C, A) are genuinely different quantities from the left-hand sides (precisions). Self-citations [19, 20, 28, 41, 42] provide context, prior special cases, and the ˜σ concept, but the mathematical derivations stand on their own. The involution existence concern raised by the skeptic is a correctness/completeness issue (whether the framework applies to all claimed setups), not a circularity issue. Score 2 reflects the minor self-citation of the ˜σ definition from the author's thesis, which is not load-bearing for the mathematical argument.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

No free parameters are fitted or introduced ad hoc. No new physical entities are postulated. The axioms are domain assumptions standard to scattering theory and fluctuation theorem frameworks, not invented for this paper. The forward-backward entropy [Eq. (4)] is defined constructively from the probability distribution and is not a new entity but a known quantity from Refs. [28, 31].

axioms (3)
  • domain assumption Average current and zero-frequency noise factorize as energy integrals over single-scattering-event statistics [Eq. (2)], valid for noninteracting systems.
    Stated in the text introducing Eq. (2) and acknowledged in Conclusions. This is the Levitov-Lesovik full counting statistics framework, standard for scattering theory but limiting the scope to noninteracting or mean-field systems.
  • domain assumption There exists an involution on the sample space such that the transported quantity q is antisymmetric [Eq. (3)] and the forward-backward entropy satisfies a fluctuation theorem [Eq. (4a)].
    Invoked in the derivation of the TUR. For time-reversal symmetric systems, the authors show this coincides with thermodynamic entropy production. The existence of such an involution for arbitrary observables in arbitrary setups is assumed, not proven in full generality.
  • domain assumption The stochastic activity a(omega) = 1 - delta_{q(omega),0} correctly generalizes dynamical activity to arbitrary transported quantities.
    Introduced in Eq. (10). The authors connect it to the classical activity in the weak-coupling limit [Eq. (14)] and note it depends on the specific quantity q of interest. The physical interpretation as a generalization of dynamical activity is supported by the examples but not independently derived from a microscopic quantum master equation.

reviewed 2026-07-08 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Uncertainty relations for arbitrary currents in coherent transport." pith.science (2026). https://pith.science/paper/7KLKMV3O

@misc{pith2026260706190,
  author       = {Pith},
  title        = {Pith review of: Uncertainty relations for arbitrary currents in coherent transport},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7KLKMV3O}},
  note         = {Machine review of arXiv:2607.06190}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

We derive thermodynamic and kinetic uncertainty relations valid for arbitrary currents in coherent, strongly coupled, linear systems out of equilibrium. Exploiting properties of the transport statistics, in particular fluctuation theorems, we identify the relevant entropy production and activity that determine the cost of precision at the level of individual scattering events. The resulting bounds include higher-order fluctuations and remain valid far from equilibrium. We illustrate our results in normal and superconducting hybrid structures, and show that their predictiveness and validity range exceeds existing formulations.

Figures

Figures reproduced from arXiv: 2607.06190 by Janine Splettstoesser, Ludovico Tesser.

Figure 1
Figure 1. Figure 1: Precision limits in NN setup. (a,d) transmission [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Precision limits in NS setup. (a,b) Charge ( [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

discussion (0)

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

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Thermodynamic bound on the Fano factor of a coherent thermoelectric heat engine

    cond-mat.mes-hall 2026-07 accept novelty 6.0

    Heat-engine operation forces a universal Fano-factor floor of F>1/2 for fermionic coherent thermoelectric transport and F>1 for bosonic or classical carriers.

Reference graph

Works this paper leans on

46 extracted references · 46 canonical work pages · cited by 1 Pith paper · 4 internal anchors

  1. [1]

    Shot noise in meso- scopic conductors,

    Ya. M. Blanter and M. B¨ uttiker, “Shot noise in meso- scopic conductors,” Phys. Rep.336, 1–166 (2000)

    work page 2000

  2. [2]

    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, 1665–1702 (2009)

    work page 2009

  3. [3]

    Current Fluctuations in Open Quantum Systems: Bridging the Gap Between Quantum Continuous Measurements and Full Counting Statistics,

    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 Quantum5, 020201 (2024)

    work page 2024

  4. [4]

    Roadmap on quantum thermodynamics,

    Steve Campbell, Irene D’Amico, Mario A Ciampini, et al., “Roadmap on quantum thermodynamics,” Quan- tum Science and Technology11, 012501 (2026)

    work page 2026

  5. [5]

    Thermodynamic Un- certainty Relation for Biomolecular Processes,

    Andre C. Barato and Udo Seifert, “Thermodynamic Un- certainty Relation for Biomolecular Processes,” Phys. 6 Rev. Lett.114, 158101 (2015)

    work page 2015

  6. [6]

    Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables,

    Juan P. Garrahan, “Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables,” Phys. Rev. E95, 032134 (2017)

    work page 2017

  7. [7]

    Kinetic uncertainty relation,

    Ivan Di Terlizzi and Marco Baiesi, “Kinetic uncertainty relation,” J. Phys. A: Math. Theor.52, 02LT03 (2018)

    work page 2018

  8. [8]

    Unified thermodynamic–kinetic uncertainty relation,

    Van Tuan Vo, Tan Van Vu, and Yoshihiko Hasegawa, “Unified thermodynamic–kinetic uncertainty relation,” J. Phys. A: Math. Theor.55, 405004 (2022)

    work page 2022

  9. [9]

    Quantum Thermodynamic Un- certainty Relation for Continuous Measurement,

    Yoshihiko Hasegawa, “Quantum Thermodynamic Un- certainty Relation for Continuous Measurement,” Phys. Rev. Lett.125, 050601 (2020)

    work page 2020

  10. [10]

    Role of Quantum Coherence in Kinetic Uncertainty Re- lations,

    Kacper Prech, Patrick P. Potts, and Gabriel T. Landi, “Role of Quantum Coherence in Kinetic Uncertainty Re- lations,” Phys. Rev. Lett.134, 020401 (2025)

    work page 2025

  11. [11]

    Ther- modynamic Bounds on Precision in Ballistic Multitermi- nal Transport,

    Kay Brandner, Taro Hanazato, and Keiji Saito, “Ther- modynamic Bounds on Precision in Ballistic Multitermi- nal Transport,” Phys. Rev. Lett.120, 090601 (2018)

    work page 2018

  12. [12]

    Assessing the validity of the thermodynamic uncertainty relation in quantum systems,

    Bijay Kumar Agarwalla and Dvira Segal, “Assessing the validity of the thermodynamic uncertainty relation in quantum systems,” Phys. Rev. B98, 155438 (2018)

    work page 2018

  13. [13]

    Thermodynamic uncer- tainty relation in quantum thermoelectric junctions,

    Junjie Liu and Dvira Segal, “Thermodynamic uncer- tainty relation in quantum thermoelectric junctions,” Phys. Rev. E99, 062141 (2019)

    work page 2019

  14. [14]

    Thermodynamic uncertainty relation in thermal transport,

    Sushant Saryal, Hava Meira Friedman, Dvira Segal, and Bijay Kumar Agarwalla, “Thermodynamic uncertainty relation in thermal transport,” Phys. Rev. E100, 042101 (2019)

    work page 2019

  15. [15]

    Broadband fre- quency filters with quantum dot chains,

    Tilmann Ehrlich and Gernot Schaller, “Broadband fre- quency filters with quantum dot chains,” Phys. Rev. B 104, 045424 (2021)

    work page 2021

  16. [16]

    Current fluctuations in nonequilibrium open quantum systems beyond weak coupling: a reaction co- ordinate approach,

    Khalak Mahadeviya, Saulo V. Moreira, Sheikh Parvez Mandal, Mahasweta Pandit, Javier Prior, and Mark T. Mitchison, “Current fluctuations in nonequilibrium open quantum systems beyond weak coupling: a reaction co- ordinate approach,” New J. Phys.28, 044511 (2026)

    work page 2026

  17. [17]

    Thermodynamic Un- certainty Relations for Coherent Transport,

    Kay Brandner and Keiji Saito, “Thermodynamic Un- certainty Relations for Coherent Transport,” Phys. Rev. Lett.135, 046302 (2025)

    work page 2025

  18. [18]

    Thermodynamic bound on current fluctuations in coherent conductors,

    Kay Brandner and Keiji Saito, “Thermodynamic bound on current fluctuations in coherent conductors,” J. Phys. A: Math. Theor.58, 435002 (2025)

    work page 2025

  19. [19]

    Combining kinetic and thermodynamic uncertainty relations in quantum transport,

    Didrik Palmqvist, Ludovico Tesser, and Janine Splettstoesser, “Combining kinetic and thermodynamic uncertainty relations in quantum transport,” Quantum Sci. Technol.10, 035059 (2025)

    work page 2025

  20. [20]

    Kinetic Uncertainty Relations for Quan- tum Transport,

    Didrik Palmqvist, Ludovico Tesser, and Janine Splettstoesser, “Kinetic Uncertainty Relations for Quan- tum Transport,” Phys. Rev. Lett.135, 166302 (2025)

    work page 2025

  21. [21]

    Quantum Kinetic Uncertainty Relations in Meso- scopic Conductors at Strong Coupling,

    Gianmichele Blasi, Ricard Ravell Rodr´ ıguez, Mykhailo Moskalets, Rosa L´ opez, and G´ eraldine Haack, “Quantum Kinetic Uncertainty Relations in Meso- scopic Conductors at Strong Coupling,” arXiv (2025), 10.48550/arXiv.2505.13200, 2505.13200

    work page internal anchor Pith review doi:10.48550/arxiv.2505.13200 2025

  22. [22]

    The role of charge in ther- modynamic uncertainty relations,

    David Christian Ohnmacht, Wolfgang Belzig, and Juan Carlos Cuevas, “The role of charge in ther- modynamic uncertainty relations,” arXiv (2025), 10.48550/arXiv.2512.20558, 2512.20558

    work page doi:10.48550/arxiv.2512.20558 2025

  23. [23]

    Quantum thermodynamic uncertainty relation and macroscopic superconducting coherence,

    Franco Mayo, Nahual Sobrino, Rosario Fazio, Fabio Tad- dei, and Michele Governale, “Quantum thermodynamic uncertainty relation and macroscopic superconducting coherence,” Phys. Rev. Res.8, 013242 (2026)

    work page 2026

  24. [24]

    Current precision in interacting hy- brid normal-superconducting systems,

    Nahual Sobrino, Fabio Taddei, Rosario Fazio, and Michele Governale, “Current precision in interacting hy- brid normal-superconducting systems,” Phys. Rev. B 113, 195407 (2026)

    work page 2026

  25. [25]

    Fluctuation Theorem Uncertainty Relation,

    Yoshihiko Hasegawa and Tan Van Vu, “Fluctuation Theorem Uncertainty Relation,” Phys. Rev. Lett.123, 110602 (2019)

    work page 2019

  26. [26]

    Thermodynamic Uncertainty Re- lations from Exchange Fluctuation Theorems,

    Andr´ e M. Timpanaro, Giacomo Guarnieri, John Goold, and Gabriel T. Landi, “Thermodynamic Uncertainty Re- lations from Exchange Fluctuation Theorems,” Phys. Rev. Lett.123, 090604 (2019)

    work page 2019

  27. [27]

    Thermodynamic uncertainty relations including measurement and feed- back,

    Patrick P. Potts and Peter Samuelsson, “Thermodynamic uncertainty relations including measurement and feed- back,” Phys. Rev. E100, 052137 (2019)

    work page 2019

  28. [28]

    thesis, Chalmers University of Technology, Sweden (2025), 544208

    Ludovico Tesser, Ph.D. thesis, Chalmers University of Technology, Sweden (2025), 544208

    work page 2025

  29. [29]

    Fundamental Precision Limits in Finite-Dimensional Quantum Thermal Machines,

    Yoshihiko Hasegawa, “Fundamental Precision Limits in Finite-Dimensional Quantum Thermal Machines,” Phys. Rev. Lett.135, 200404 (2025)

    work page 2025

  30. [30]

    Tightening the thermodynamic uncertainty re- lations with null-entropy events: What we learn when nothing happens,

    Abhaya S. Hegde, Andr´ e M. Timpanaro, and Gabriel T. Landi, “Tightening the thermodynamic uncertainty re- lations with null-entropy events: What we learn when nothing happens,” Phys. Rev. E113, 034111 (2026)

    work page 2026

  31. [31]

    Univer- sal Precision Limits in General Open Quantum Systems,

    Tan Van Vu, Ryotaro Honma, and Keiji Saito, “Univer- sal Precision Limits in General Open Quantum Systems,” Phys. Rev. Lett.136, 190401 (2026)

    work page 2026

  32. [32]

    Moskalets,Scattering Matrix Approach to Non-Stationary Quantum Transport(World Scientific Publishing Company, London, England, UK, 2011)

    Michael V. Moskalets,Scattering Matrix Approach to Non-Stationary Quantum Transport(World Scientific Publishing Company, London, England, UK, 2011)

    work page 2011

  33. [33]

    Charge dis- tribution in quantum shot noise,

    Leonid S. Levitov and Gordey B. Lesovik, “Charge dis- tribution in quantum shot noise,” J. Exp. Theor. Phys. 58, 230–230 (1993)

    work page 1993

  34. [34]

    Full Counting Statistics of Electron Transfer between Superconductors,

    W. Belzig and Yu. V. Nazarov, “Full Counting Statistics of Electron Transfer between Superconductors,” Phys. Rev. Lett.87, 197006 (2001)

    work page 2001

  35. [35]

    Irreversible entropy production: From classical to quantum,

    Gabriel T. Landi and Mauro Paternostro, “Irreversible entropy production: From classical to quantum,” Rev. Mod. Phys.93, 035008 (2021)

    work page 2021

  36. [36]

    Philipp Strasberg,Quantum Stochastic Thermodynamics (Oxford University Press, Oxford, England, UK, 2022)

    work page 2022

  37. [37]

    Unified Thermodynamic Uncertainty Rela- tions in Linear Response,

    Katarzyna Macieszczak, Kay Brandner, and Juan P. Garrahan, “Unified Thermodynamic Uncertainty Rela- tions in Linear Response,” Phys. Rev. Lett.121, 130601 (2018)

    work page 2018

  38. [38]

    Power, Efficiency and Fluctuations in a Quantum Point Contact as Steady-State Thermoelectric Heat Engine,

    Sara Kheradsoud, Nastaran Dashti, Maciej Misiorny, Patrick P. Potts, Janine Splettstoesser, and Peter Samuelsson, “Power, Efficiency and Fluctuations in a Quantum Point Contact as Steady-State Thermoelectric Heat Engine,” Entropy21, 777 (2019)

    work page 2019

  39. [39]

    Comment on "Fluctuation Theorem Uncertainty Relation" and "Thermodynamic Uncertainty Relations from Exchange Fluctuation Theorems"

    Yunxin Zhang, “Comment on ”Fluctuation Theorem Un- certainty Relation” and ”Thermodynamic Uncertainty Relations from Exchange Fluctuation Theorems”,” arXiv (2019), 10.48550/arXiv.1910.12862, 1910.12862

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1910.12862 2019

  40. [40]

    Thermokinetic Uncertainty Relations and Dynamical Activities in Quantum Systems,

    Didrik Palmqvist, “Thermokinetic Uncertainty Relations and Dynamical Activities in Quantum Systems,” (2026), 551724

    work page 2026

  41. [41]

    Susceptibility-kinetic uncertainty relations for quantum systems

    Didrik Palmqvist, Ludovico Tesser, and Janine Splettstoesser, “Susceptibility-kinetic uncertainty relations for quantum systems,” arXiv (2026), 10.48550/arXiv.2607.01035, 2607.01035

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2607.01035 2026

  42. [42]

    Stochastic entropy production in scattering theory

    Ludovico Tesser, Henning Kirchberg, Matteo Ac- ciai, and Janine Splettstoesser, “Stochastic en- tropy production in scattering theory,” arXiv (2026), 10.48550/arXiv.2604.10322, 2604.10322

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2604.10322 2026

  43. [43]

    General Bounds on Electronic Shot 7 Noise in the Absence of Currents,

    Jakob Eriksson, Matteo Acciai, Ludovico Tesser, and Ja- nine Splettstoesser, “General Bounds on Electronic Shot 7 Noise in the Absence of Currents,” Phys. Rev. Lett.127, 136801 (2021)

    work page 2021

  44. [44]

    Tran- sition from metallic to tunneling regimes in supercon- ducting microconstrictions: Excess current, charge im- balance, and supercurrent conversion,

    G. E. Blonder, M. Tinkham, and T. M. Klapwijk, “Tran- sition from metallic to tunneling regimes in supercon- ducting microconstrictions: Excess current, charge im- balance, and supercurrent conversion,” Phys. Rev. B25, 4515–4532 (1982)

    work page 1982

  45. [45]

    Thermodynamic un- certainty relations for systems with broken time reversal symmetry: The case of superconducting hybrid systems,

    Fabio Taddei and Rosario Fazio, “Thermodynamic un- certainty relations for systems with broken time reversal symmetry: The case of superconducting hybrid systems,” Phys. Rev. B108, 115422 (2023)

    work page 2023

  46. [46]

    Information Thermodynamics in a Quantum Dot Szi- lard Engine - Experimentally Investigating Fluctuation Theorems and Thermodynamic Uncertainty Relations,

    David Barker, Sebastian Lehmann, Kimberly A. Dick, Peter Samuelsson, Ville Maisi, and Patrick P. Potts, “Information Thermodynamics in a Quantum Dot Szi- lard Engine - Experimentally Investigating Fluctuation Theorems and Thermodynamic Uncertainty Relations,” arXiv (2025), 10.48550/arXiv.2511.08541, 2511.08541

    work page doi:10.48550/arxiv.2511.08541 2025

This paper was first reviewed by glm-5.2 on July 8, 2026.