Information-thermodynamic bounds on precision in interacting quantum systems

TL;DR

This work extends thermodynamic uncertainty relations to interacting multipartite quantum systems by introducing a quantum TKUR that bounds local current fluctuations in terms of partial entropy production, partial dynamical activity, and information flow between subsystems, with a quantum-coherence correction. It derives a corollary quantum TUR and a multidimensional bound, valid for arbitrary finite times and states, revealing that information exchange can enhance precision even with limited local dissipation. The authors validate the results numerically on an autonomous quantum Maxwell's demon and a quantum clock, showing that quantum coherence and information flow can fundamentally alter precision limits and enable high-performance quantum thermal machines. The findings illuminate the functional role of information flow in quantum thermodynamics and offer a framework for optimizing currents in complex open quantum systems, with potential implications for quantum technologies exploiting coherence and information processing.The paper develops a rigorous information-thermodynamic framework for open quantum systems, introducing local entropy production and information flow terms; it shows how these quantities constrain subsystem currents under GKSL dynamics with local detailed balance. It then derives a quantum TKUR that tightens the classical bounds by including a coherence-dependent correction and demonstrates a corresponding multidimensional bound that optimizes over linear combinations of currents. The approach connects quantum Fisher information to thermodynamic quantities via a quantum Cramér-Rao argument, enabling a principled derivation of the bounds and their dependence on information flow. Through detailed numerical studies of autonomous Maxwellian and clock models, the work demonstrates how information flow and coherence can suppress fluctuations at finite dissipation, offering design principles for quantum engines and clocks operating near fundamental thermodynamic limits.

Abstract

The thermodynamic uncertainty relation quantifies a trade-off between the relative fluctuations of trajectory currents and the thermodynamic cost, indicating that the current precision is fundamentally constrained by entropy production. In classical bipartite systems, it has been shown that information flow between subsystems can enhance the current precision alongside thermodynamic dissipation. In this study, we investigate how information flow, local dissipation, and quantum effects jointly constrain current fluctuations within a subsystem of interacting quantum systems. Unlike classical bipartite systems, quantum subsystems can exhibit simultaneous state changes and maintain quantum coherence, which fundamentally alters the precision-dissipation trade-off. For this general setting, we derive a quantum thermokinetic uncertainty relation for interacting multipartite systems, establishing a thermodynamic trade-off between current fluctuations, information flow, local dissipation, and quantum effects. Our analysis shows that, in addition to local dissipation, both information exchange and quantum coherence play essential roles in suppressing current fluctuations. These results have important implications for the performance of quantum thermal machines, such as information-thermodynamic engines and quantum clocks. We validate our theoretical findings through numerical simulations on two representative models: an autonomous quantum Maxwell's demon and a quantum clock. These results extend uncertainty relations to multipartite open quantum systems and elucidate the functional role of information flow in fluctuation suppression.

Figures (5)

• Figure 1: Schematic of interacting quantum systems. The system consists of $M$ subsystems $(X_1, \dots, X_M)$, where each subsystem $X_i$ is coupled to a set of reservoirs $\{\alpha_i\}$, characterized by inverse temperatures and chemical potentials $\{\beta_{\alpha_i}, \mu_{\alpha_i}\}$. Each subsystem dissipates heat into its environment and interacts with the others, giving rise to inter-subsystem information flow.
• Figure 2: (a) Schematic illustration of the autonomous quantum Maxwell's demon, composed of two exchange-coupled quantum dots, each coupled to spin-polarized electronic leads arranged in an antiparallel configuration. (b), (c) Numerical verification of the quantum TUR in the steady state. In the upper panels, the solid, dashed, and dash-dotted lines represent the information flow rate $\dot I_1$, local entropy production rate $\dot \Sigma_1$, and partial entropy production rate $\dot S_1^{\rm tot}=\dot{\Sigma}_1 - \dot{I}_1 \ge 0$, respectively. In the lower panels, the solid, dashed, and dash-dotted lines correspond to the quality factors $F_1$ and $F_1'$, and the relative fluctuation $\mathop{\mathrm{Var}}\nolimits[\mathcal{J}_1]/\ev{\mathcal{J}_1}^2$. The electrochemical potentials $\mu_{1L}=-\mu_{1R}$ or the exchange coupling $J$ is varied, whereas the remaining parameters are set as follows: $\beta = 0.01$, $J = 10$, $\mu_{1L} = -\mu_{1R}= 0$, $\mu_{2L} = -\mu_{2R} = -30$, $\gamma^{\downarrow}_{1L} = \gamma^{\uparrow}_{1R} = \gamma^{\uparrow}_{2L} = \gamma^{\downarrow}_{2R} = 0$, and $\tau = 10$. All remaining coupling strengths are set to $\gamma^{\sigma}_{i \nu} = 1$.
• Figure 3: Numerical plots of the $l_1$-norm of quantum coherence $\mathcal{C}$ (dashed lines) and the correction term $\delta_{\mathcal{J}_1}$ (solid lines): (a) As functions of the electrochemical potentials $\mu_{1L} = -\mu_{1R}$; (b) As functions of the coupling strength $\gamma_2$. All other parameters are fixed as in Fig. \ref{['fig:Maxwell']}.
• Figure 4: (a) Schematic of the autonomous quantum clock, composed of a two-qubit heat engine and a four-level ladder, each coupled to thermal reservoirs. (b), (c), (d) Numerical validation of the quantum TUR \ref{['eq:main.result.2']} in the steady state. In the upper panels, the solid, dashed, and dash-dotted lines correspond to the information flow rate $\dot I_w$, local entropy production rate $\dot \Sigma_w$, and partial entropy production rate $\dot S_w^{\rm tot}=\dot\Sigma_w-\dot I_w\ge 0$, respectively. In the lower panels, the solid, dashed, and dash-dotted lines represent the quality factors $F_w$ and $F_w'$, and the relative fluctuation $\mathop{\mathrm{Var}}\nolimits[\mathcal{J}_w]/\ev{\mathcal{J}_w}^2$, respectively. The inverse temperatures are varied as indicated, while the remaining parameters are fixed: $\beta_c=1$, $\beta_h=10^{-3}$, $\beta_w=0.1$, $E_c=E_w=1$, $E_h=E_c+E_w$, $g=5$, $\gamma_c=\gamma_h=\gamma_w=1$, and $\tau=10$.
• Figure 5: Numerical plots of the $l_1$-norm of quantum coherence $\mathcal{C}$ (dashed lines) and the correction term $\delta_{\mathcal{J}_w}$ (solid lines): (a) As functions of the inverse temperature $\beta_c$; (b) As functions of the coupling strengths $\{\gamma_c, \gamma_h\}$. All other parameters are fixed as in Fig. \ref{['fig:clock']}.