Physica C Superconductivity

Planckian bounds from local uncertainty relations

Zohar Nussinov, Saurish Chakrabarty

Published Jul 15, 2025• 0 citations

Abstract

We introduce “ local uncertainty relations ” in thermal quantum many-body systems from which fundamental bounds can be derived. These inequalities imply rigorous universal non-relativistic speed limits (independent of interaction range) and, as we focus on in the current work, bounds associated with transport (e.g., the diffusion constant and shear viscosity). Using the chaos bounds and other considerations, we introduce simplified non-rigorous universal transport coefficient inequalities and compare our resulting bounds against experimental data.

DOI: 10.1016/j.physc.2025.1354755

Related papers

Planckian Bounds From Local Uncertainty Relations

Saurish Chakrabarty, Zohar Nussinov

We introduce ``local uncertainty relations'' in thermal many-body systems, from which fundamental bounds in quantum systems can be derived. These lead to universal non-relativistic speed limits (independent of interaction range) and transport coefficient bounds (e.g., those of the diffusion constant and viscosity) that are compared against experimental data.

arXiv:2502.10129Feb 14, 20250 citations

Quantum equilibration and measurements -- bounds on speeds, Lyapunov exponents, and transport coefficients obtained from the uncertainty relations and their comparison with experimental data

Saurish Chakrabarty, Zohar Nussinov

arXiv:2303.00021Feb 28, 20230 citations

Universal Velocity, Minimal Transport Coefficient, "Collapse" Times to Equilibrium States, and Other Bounds in Quantum Thermal Systems

Zohar Nussinov, Saurish Chakrabarty

Jul 22, 20210 citations

Planckian bound on the local equilibration time

Marvin Qi, Alexey Milekhin, Luca V. Delacrétaz

arXiv:2602.17638Feb 19, 20260 citations

Constraints on hydrodynamics from many-body quantum chaos

Andrew Lucas

arXiv:1710.01005Oct 3, 201732 citations

Bounds in nonequilibrium quantum dynamics

Zongping Gong, Ryusuke Hamazaki

arXiv:2202.02011International Journal of Modern Physics BSep 26, 202246 citations

Physica C Superconductivity

Planckian bounds from local uncertainty relations

Zohar Nussinov, Saurish Chakrabarty

Published Jul 15, 2025• 0 citations

Publisher

Abstract

DOI: 10.1016/j.physc.2025.1354755

Related papers

Planckian Bounds From Local Uncertainty Relations

Saurish Chakrabarty, Zohar Nussinov

arXiv:2502.10129Feb 14, 20250 citations

Quantum equilibration and measurements -- bounds on speeds, Lyapunov exponents, and transport coefficients obtained from the uncertainty relations and their comparison with experimental data

Saurish Chakrabarty, Zohar Nussinov

We discuss our recent study of local quantum mechanical uncertainty relations in quantum many body systems. These lead to fundamental bounds for quantities such as the speed, acceleration, relaxation times, spatial gradients and the Lyapunov exponents. We additionally obtain bounds on various transport coefficients like the viscosity, the diffusion constant, and the thermal conductivity. Some of these bounds are related to earlier conjectures, such as the bound on chaos by Maldacena, Shenker and Stanford while others are new. Our approach is a direct way of obtaining exact bounds in fairly general settings. We employ uncertainty relations for local quantities from which we strip off irrelevant terms as much as possible, thereby removing non-local terms. To gauge the utility of our bounds, we briefly compare their numerical values with typical values available from experimental data. In various cases, approximate simplified variants of the bounds that we obtain can become fairly tight, i.e., comparable to experimental values. These considerations lead to a minimal time for thermal equilibrium to be achieved. Building on a conjectured relation between quantum measurements and equilibration, our bounds, far more speculatively, suggest a minimal time scale for measurements to stabilize to equilibrium values.We discuss our recent study of local quantum mechanical uncertainty relations in quantum many body systems. These lead to fundamental bounds for quantities such as the speed, acceleration, relaxation times, spatial gradients and the Lyapunov exponents. We additionally obtain bounds on various transport coefficients like the viscosity, the diffusion constant, and the thermal conductivity. Some of these bounds are related to earlier conjectures, such as the bound on chaos by Maldacena, Shenker and Stanford while others are new. Our approach is a direct way of obtaining exact bounds in fairly general settings. We employ uncertainty relations for local quantities from which we strip off irrelevant terms as much as possible, thereby removing non-local terms. To gauge the utility of our bounds, we briefly compare their numerical values with typical values available from experimental data. In various cases, approximate simplified variants of the bounds that we obtain can become fairly tight, i.e., comparable to experimental values. These considerations lead to a minimal time for thermal equilibrium to be achieved. Building on a conjectured relation between quantum measurements and equilibration, our bounds, far more speculatively, suggest a minimal time scale for measurements to stabilize to equilibrium values.

arXiv:2303.00021Feb 28, 20230 citations

Universal Velocity, Minimal Transport Coefficient, "Collapse" Times to Equilibrium States, and Other Bounds in Quantum Thermal Systems

Zohar Nussinov, Saurish Chakrabarty

Using local uncertainty relations in thermal many body systems, we illustrate that there exist universal speed limit (regardless of interaction range), bounds on acceleration or force/stress, acceleration or material stress rates, diffusion constant, viscosity, other transport coefficients, electromagnetic or other gauge field strengths, correlation functions of arbitrary spatio-temporal derivatives, Lyapunov exponents, thermalization times, and transition times between orthogonal states in non-relativistic quantum thermal systems, and derive analogs of the Ioffe-Regel limit. In the $\hbar \to 0$ limit, all of our bounds either diverge (e.g., our speed and acceleration limit) or vanish (as in, e.g., our viscosity and diffusion constant bounds). Our inequalities hold at all temperatures and, as corollaries, imply general power law bounds on response functions at both asymptotically high and low temperatures. Our results shed light on measurements and on how apparent nearly instantaneous effective collapse to an eigenstate may arise in macroscopic interacting many body quantum systems.Using local uncertainty relations in thermal many body systems, we illustrate that there exist universal speed limit (regardless of interaction range), bounds on acceleration or force/stress, acceleration or material stress rates, diffusion constant, viscosity, other transport coefficients, electromagnetic or other gauge field strengths, correlation functions of arbitrary spatio-temporal derivatives, Lyapunov exponents, thermalization times, and transition times between orthogonal states in non-relativistic quantum thermal systems, and derive analogs of the Ioffe-Regel limit. In the $\hbar \to 0$ limit, all of our bounds either diverge (e.g., our speed and acceleration limit) or vanish (as in, e.g., our viscosity and diffusion constant bounds). Our inequalities hold at all temperatures and, as corollaries, imply general power law bounds on response functions at both asymptotically high and low temperatures. Our results shed light on measurements and on how apparent nearly instantaneous effective collapse to an eigenstate may arise in macroscopic interacting many body quantum systems.

Jul 22, 20210 citations

Planckian bound on the local equilibration time

Marvin Qi, Alexey Milekhin, Luca V. Delacrétaz

The local equilibration time $τ_{\rm eq}$ of quantum many-body systems is conjectured to be bounded below by the Planckian time $\hbar /T$ . We formalize this conjecture by defining $τ_{\rm eq}$ as the time scale at which a hydrodynamic description emerges for conserved densities. Drawing on analytic properties of real time thermal correlators, we establish a rigorous lower bound $τ_{\rm eq} \geq α\hbar /T$ on the onset of hydrodynamic behavior in a `regulated' thermal two-point function. The dimensionless coefficient $α$ depends only on dimensionality and the type of hydrodynamic or diffusive behavior that emerges, and is independent of the thermalization mechanism or other microscopic details. This bound applies universally to local quantum many-body systems, with or without a quasiparticle description, including in the presence of inelastic scattering.The local equilibration time $τ_{\rm eq}$ of quantum many-body systems is conjectured to be bounded below by the Planckian time $\hbar /T$. We formalize this conjecture by defining $τ_{\rm eq}$ as the time scale at which a hydrodynamic description emerges for conserved densities. Drawing on analytic properties of real time thermal correlators, we establish a rigorous lower bound $τ_{\rm eq} \geq α\hbar /T$ on the onset of hydrodynamic behavior in a `regulated' thermal two-point function. The dimensionless coefficient $α$ depends only on dimensionality and the type of hydrodynamic or diffusive behavior that emerges, and is independent of the thermalization mechanism or other microscopic details. This bound applies universally to local quantum many-body systems, with or without a quasiparticle description, including in the presence of inelastic scattering.

arXiv:2602.17638Feb 19, 20260 citations

Constraints on hydrodynamics from many-body quantum chaos

Andrew Lucas

Is the hydrodynamics of an interacting many-body system fundamentally limited by basic principles of quantum mechanics? Starting with the conjecture that viscosity is at least as large as entropy density (as measured in fundamental units), there has been a long search for a precise answer to this question. In this work, we identify a simple relationship between hydrodynamics and many-body quantum chaos in a broad class of experimentally realizable systems. Consistency with the quantum butterfly effect leads to upper bounds on the speed of sound and diffusion constants of hydrodynamics. These bounds link two very different theories of quantum many-body dynamics, clarify the relationship between classical hydrodynamics and quantum information loss, and provide a simple way to constrain theories of thermalization and quantum chaos in experiments.Is the hydrodynamics of an interacting many-body system fundamentally limited by basic principles of quantum mechanics? Starting with the conjecture that viscosity is at least as large as entropy density (as measured in fundamental units), there has been a long search for a precise answer to this question. In this work, we identify a simple relationship between hydrodynamics and many-body quantum chaos in a broad class of experimentally realizable systems. Consistency with the quantum butterfly effect leads to upper bounds on the speed of sound and diffusion constants of hydrodynamics. These bounds link two very different theories of quantum many-body dynamics, clarify the relationship between classical hydrodynamics and quantum information loss, and provide a simple way to constrain theories of thermalization and quantum chaos in experiments.

arXiv:1710.01005Oct 3, 201732 citations

Bounds in nonequilibrium quantum dynamics

Zongping Gong, Ryusuke Hamazaki

We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical stochastic systems. We start from the speed limits, the universal bounds on the speeds of (either quantum or classical) dynamical evolutions. We then turn to review the bounds that address how good and how long would a quantum system equilibrate or thermalize. Afterward, we focus on the stringent constraint set by locality in many-body systems, rigorously formalized as the Lieb–Robinson bound. We also review the bounds related to the dynamics of entanglement, a genuine quantum property. Apart from some other miscellaneous topics, several notable error bounds for approximated quantum dynamics are discussed. While far from comprehensive, this topical review covers a considerable amount of recent progress and thus could hopefully serve as a convenient starting point and up-to-date guidance for interested readers.We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical stochastic systems. We start from the speed limits, the universal bounds on the speeds of (either quantum or classical) dynamical evolutions. We then turn to review the bounds that address how good and how long would a quantum system equilibrate or thermalize. Afterward, we focus on the stringent constraint set by locality in many-body systems, rigorously formalized as the Lieb–Robinson bound. We also review the bounds related to the dynamics of entanglement, a genuine quantum property. Apart from some other miscellaneous topics, several notable error bounds for approximated quantum dynamics are discussed. While far from comprehensive, this topical review covers a considerable amount of recent progress and thus could hopefully serve as a convenient starting point and up-to-date guidance for interested readers.

arXiv:2202.02011International Journal of Modern Physics BSep 26, 202246 citations

\hbar \to 0

limit, all of our bounds either diverge (e.g., our speed and acceleration limit) or vanish (as in, e.g., our viscosity and diffusion constant bounds). Our inequalities hold at all temperatures and, as corollaries, imply general power law bounds on response functions at both asymptotically high and low temperatures. Our results shed light on measurements and on how apparent nearly instantaneous effective collapse to an eigenstate may arise in macroscopic interacting many body quantum systems.

The local equilibration time

τ_{\rm eq}

of quantum many-body systems is conjectured to be bounded below by the Planckian time

\hbar /T

. We formalize this conjecture by defining

τ_{\rm eq}

as the time scale at which a hydrodynamic description emerges for conserved densities. Drawing on analytic properties of real time thermal correlators, we establish a rigorous lower bound

τ_{\rm eq} \geq α\hbar /T

on the onset of hydrodynamic behavior in a `regulated' thermal two-point function. The dimensionless coefficient

α

depends only on dimensionality and the type of hydrodynamic or diffusive behavior that emerges, and is independent of the thermalization mechanism or other microscopic details. This bound applies universally to local quantum many-body systems, with or without a quasiparticle description, including in the presence of inelastic scattering.