Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. E

Matrix thermodynamic uncertainty relation for non-Abelian charge transport

Anonymous

Published Aug 4, 2026• 0 citations
Publisher

Abstract

Thermodynamic uncertainty relations (TURs) bound current precision by entropy production, but transport of noncommuting (non-Abelian) charges lacks a single joint classical record of all current components. We derive an operational, process-level matrix TUR for this setting from the entropy production Σ=D(ρ_{SE}^{'}∥ρ_{S}^{'}⊗ρ_{E}). Isolating the bath divergence D_{bath}=D(ρ_{E}^{'}∥ρ_{E}), we prove a fully nonlinear, saturable lower bound valid for arbitrary current vectors Δq: D_{bath}≥B(Δq,V,V^{'}), where the bound depends only on the transported-charge signal Δq and on the pre- and postcollision covariance matrices V and V^{'} reconstructed from separate probe measurement settings. In the small-fluctuation regime D_{bath}≥1/2Δq^{T}V^{-1}Δq+O(∥Δq∥^{4}), while beyond linear response the full integral bound remains valid. Numerical strong-coupling qubit collisions illustrate the bound and its near-saturation using only local measurements on the bath probe.

DOI
10.1103/q2yg-rp7q

Related papers

Matrix Thermodynamic Uncertainty Relation for Non-Abelian Charge Transport

Domingos S. P. Salazar

Thermodynamic uncertainty relations (TURs) bound the precision of currents by entropy production, but quantum transport of noncommuting (non-Abelian) charges challenges standard formulations because different charge components cannot be monitored within a single classical frame. We derive a process-level matrix TUR starting from the operational entropy production $Σ= D(ρ'_{SE}\|ρ'_S\!\otimes\!ρ_E)$. Isolating the experimentally accessible bath divergence $D_{\mathrm{bath}}=D(ρ'_E\|ρ_E)$, we prove a fully nonlinear, saturable lower bound valid for arbitrary current vectors $Δq$: $D_{\mathrm{bath}} \ge B(Δq,V,V')$, where the bound depends only on the transported-charge signal $Δq$ and the pre/post collision covariance matrices $V$ and $V'$. In the small-fluctuation regime $D_{\mathrm{bath}}\geq\frac12\,Δq^{\mathsf T}V^{-1}Δq+O(\|Δq\|^4)$, while beyond linear response it remains accurate. Numerical strong-coupling qubit collisions illustrate the bound and demonstrate near-saturation across broad parameter ranges using only local measurements on the bath probe.

quant-pharXiv:2512.24956•Jan 1, 2026•0 citations

Non-equilibrium thermodynamics of precision through a quantum-centric computation

Mário Motta, Antonio Mezzacapo, Giacomo Guarnieri

Thermodynamic uncertainty relations (TURs) are a set of inequalities expressing a fundamental trade-off between precision and dissipation in non-equilibrium classical and quantum thermodynamic processes. TURs show that achieving low fluctuations in a thermodynamic quantity (e.g., heat or work) requires a minimum entropy production, with profound implications for the efficiency of biological and artificial thermodynamic processes. The accurate evaluation of TURs is a necessary requirement to quantify the fluctuation and dissipation entailed by a thermodynamic process, and ultimately to optimize the performance of quantum devices, whose operation is fundamentally a quantum thermodynamic process. Here, we simulate TURs in a transverse-field Ising model subjected to a time-dependent driving protocol, using quantum and classical computers in concert. Varying the duration and strength of the drive as well as the system size, we verify the validity of TURs, identify quantum signatures in the work statistics within the linear response regime, and observe TUR saturation in the high-temperature limit.

arXiv:2503.03868•Mar 5, 2025•0 citations

Quantum relative entropy uncertainty relation

Domingos S. P. Salazar

For classic systems, the thermodynamic uncertainty relation (TUR) states that the fluctuations of a current have a lower bound in terms of the entropy production. Some TURs are rooted in information theory, particularly derived from relations between observations (mean and variance) and dissimilarities, such as the Kullback-Leibler divergence, which plays the role of entropy production in stochastic thermodynamics. We generalize this idea for quantum systems, where we find a lower bound for the uncertainty of quantum observables given in terms of the quantum relative entropy. We apply the result to obtain a quantum thermodynamic uncertainty relation in terms of the quantum entropy production, valid for arbitrary dynamics and nonthermal environments.

arXiv:2309.09990•Physical review. E•Jan 19, 2024•7 citations

Universal Statistics of Charge Exchanges in Non-Abelian Quantum Transport

Matteo Scandi, Gonzalo Manzano

We derive detailed and intergral fluctuation relations as well as a thermodynamic uncertainty relation constraining the exchange statistics of an arbitrary number of noncommuting conserved quantities among two quantum systems in transport setups arbitrary far from equilibrium. These universal relations, valid without the need of any efficacy parameter, extend the well-known heat exchange fluctuation theorems for energy and particle transport to the case of non-Abelian quantum transport, where the noncommutativity of the charges allows going beyond standard thermodynamic behavior. In particular, we show that this can lead to enhanced precision in the current fluctuations, and it allows for the inversion of all currents against their affinity biases.

arXiv:2508.15540•Physical Review Letters•Mar 25, 2026•0 citations

Thermodynamic uncertainty relation under continuous measurement and feedback with quantum-classical-transfer entropy

Kaito Tojo, Takahiro Sagawa, Ken Funo

We derive a thermodynamic uncertainty relation (TUR) under quantum continuous measurement and feedback control. By incorporating the quantum-classical-transfer entropy, which quantifies the information gained by continuous measurement, we show that the precision of currents is constrained by information-thermodynamic costs such as the entropy production and information gain. Our result shows that information gain has the potential to enhance the precision of currents beyond the bounds set by the conventional TUR. We illustrate the bound with a driven two-level system under continuous measurement and feedback, demonstrating that feedback achieves higher precision of currents while suppressing the entropy production.

cond-mat.stat-mechCross-listedarXiv:2602.23110•Feb 27, 2026•0 citations

Combining kinetic and thermodynamic uncertainty relations in quantum transport

Didrik Palmqvist, Ludovico Tesser, Janine Splettstoesser

Abstract We study the fluctuations of generic currents in multi-terminal, multi-channel coherent quantum transport settings. In the quantum regime, these fluctuations and the resulting precision differ strongly depending on whether the device is of fermionic or bosonic nature. Using scattering theory, we show that the precision is bounded by constraints set by the entropy production and by the activity in the spirit of thermodynamic or kinetic uncertainty relations, valid for fermionic and bosonic quantum systems also in the absence of time-reversal symmetry. Furthermore, we derive a combined thermodynamic kinetic uncertainty relation, which is tight over a wide range of parameters and can hence predict the reachable precision of a device. Since these constraints can be expressed in terms of observables accessible in transport measurements, such as currents and bandwidth, we foresee that the tight thermodynamic kinetic uncertainty-like bounds are also useful as an inference tool: they can be exploited to estimate entropy production from transport observables, such as the charge current and its noise, which are more easily accessible in experiment.

arXiv:2504.04980•Quantum Science and Technology•Jun 19, 2025•6 citations
Thermodynamic uncertainty relations (TURs) bound current precision by entropy production, but transport of noncommuting (non-Abelian) charges lacks a single joint classical record of all current components. We derive an operational, process-level matrix TUR for this setting from the entropy production Σ=D(ρ_{SE}^{'}∥ρ_{S}^{'}⊗ρ_{E}). Isolating the bath divergence D_{bath}=D(ρ_{E}^{'}∥ρ_{E}), we prove a fully nonlinear, saturable lower bound valid for arbitrary current vectors Δq: D_{bath}≥B(Δq,V,V^{'}), where the bound depends only on the transported-charge signal Δq and on the pre- and postcollision covariance matrices V and V^{'} reconstructed from separate probe measurement settings. In the small-fluctuation regime D_{bath}≥1/2Δq^{T}V^{-1}Δq+O(∥Δq∥^{4}), while beyond linear response the full integral bound remains valid. Numerical strong-coupling qubit collisions illustrate the bound and its near-saturation using only local measurements on the bath probe.
Thermodynamic uncertainty relations (TURs) bound the precision of currents by entropy production, but quantum transport of noncommuting (non-Abelian) charges challenges standard formulations because different charge components cannot be monitored within a single classical frame. We derive a process-level matrix TUR starting from the operational entropy production Σ=D(ρSE′∥ρS′ ⁣⊗ ⁣ρE)Σ= D(ρ'_{SE}\|ρ'_S\!\otimes\!ρ_E)Σ=D(ρSE′​∥ρS′​⊗ρE​). Isolating the experimentally accessible bath divergence Dbath=D(ρE′∥ρE)D_{\mathrm{bath}}=D(ρ'_E\|ρ_E)Dbath​=D(ρE′​∥ρE​), we prove a fully nonlinear, saturable lower bound valid for arbitrary current vectors ΔqΔqΔq: Dbath≥B(Δq,V,V′)D_{\mathrm{bath}} \ge B(Δq,V,V')Dbath​≥B(Δq,V,V′), where the bound depends only on the transported-charge signal ΔqΔqΔq and the pre/post collision covariance matrices VVV and V′V'V′. In the small-fluctuation regime Dbath≥12 ΔqTV−1Δq+O(∥Δq∥4)D_{\mathrm{bath}}\geq\frac12\,Δq^{\mathsf T}V^{-1}Δq+O(\|Δq\|^4)Dbath​≥21​ΔqTV−1Δq+O(∥Δq∥4), while beyond linear response it remains accurate. Numerical strong-coupling qubit collisions illustrate the bound and demonstrate near-saturation across broad parameter ranges using only local measurements on the bath probe.
Thermodynamic uncertainty relations (TURs) are a set of inequalities expressing a fundamental trade-off between precision and dissipation in non-equilibrium classical and quantum thermodynamic processes. TURs show that achieving low fluctuations in a thermodynamic quantity (e.g., heat or work) requires a minimum entropy production, with profound implications for the efficiency of biological and artificial thermodynamic processes. The accurate evaluation of TURs is a necessary requirement to quantify the fluctuation and dissipation entailed by a thermodynamic process, and ultimately to optimize the performance of quantum devices, whose operation is fundamentally a quantum thermodynamic process. Here, we simulate TURs in a transverse-field Ising model subjected to a time-dependent driving protocol, using quantum and classical computers in concert. Varying the duration and strength of the drive as well as the system size, we verify the validity of TURs, identify quantum signatures in the work statistics within the linear response regime, and observe TUR saturation in the high-temperature limit.
For classic systems, the thermodynamic uncertainty relation (TUR) states that the fluctuations of a current have a lower bound in terms of the entropy production. Some TURs are rooted in information theory, particularly derived from relations between observations (mean and variance) and dissimilarities, such as the Kullback-Leibler divergence, which plays the role of entropy production in stochastic thermodynamics. We generalize this idea for quantum systems, where we find a lower bound for the uncertainty of quantum observables given in terms of the quantum relative entropy. We apply the result to obtain a quantum thermodynamic uncertainty relation in terms of the quantum entropy production, valid for arbitrary dynamics and nonthermal environments.
We derive detailed and intergral fluctuation relations as well as a thermodynamic uncertainty relation constraining the exchange statistics of an arbitrary number of noncommuting conserved quantities among two quantum systems in transport setups arbitrary far from equilibrium. These universal relations, valid without the need of any efficacy parameter, extend the well-known heat exchange fluctuation theorems for energy and particle transport to the case of non-Abelian quantum transport, where the noncommutativity of the charges allows going beyond standard thermodynamic behavior. In particular, we show that this can lead to enhanced precision in the current fluctuations, and it allows for the inversion of all currents against their affinity biases.
We derive a thermodynamic uncertainty relation (TUR) under quantum continuous measurement and feedback control. By incorporating the quantum-classical-transfer entropy, which quantifies the information gained by continuous measurement, we show that the precision of currents is constrained by information-thermodynamic costs such as the entropy production and information gain. Our result shows that information gain has the potential to enhance the precision of currents beyond the bounds set by the conventional TUR. We illustrate the bound with a driven two-level system under continuous measurement and feedback, demonstrating that feedback achieves higher precision of currents while suppressing the entropy production.
Abstract We study the fluctuations of generic currents in multi-terminal, multi-channel coherent quantum transport settings. In the quantum regime, these fluctuations and the resulting precision differ strongly depending on whether the device is of fermionic or bosonic nature. Using scattering theory, we show that the precision is bounded by constraints set by the entropy production and by the activity in the spirit of thermodynamic or kinetic uncertainty relations, valid for fermionic and bosonic quantum systems also in the absence of time-reversal symmetry. Furthermore, we derive a combined thermodynamic kinetic uncertainty relation, which is tight over a wide range of parameters and can hence predict the reachable precision of a device. Since these constraints can be expressed in terms of observables accessible in transport measurements, such as currents and bandwidth, we foresee that the tight thermodynamic kinetic uncertainty-like bounds are also useful as an inference tool: they can be exploited to estimate entropy production from transport observables, such as the charge current and its noise, which are more easily accessible in experiment.