What Does Planckian Dissipation Mean?

The question is: Is Planckian dissipation a bound, a scaling relation, a transport timescale, or a phenomenological pattern within explicitly stated systems? The recurring scale

$$\tau_{\mathrm P}=\frac{\hbar}{k_B T}$$

is striking because it uses only temperature and quantum units. Its appearance does not by itself identify which excitation relaxes, which correlator was fitted, or whether the coefficient is universal. Those distinctions decide whether “Planckian” is a law, a mechanism, or dimensional shorthand.

Evidence cutoff. 11 August 2026.

Required background. Strange-Metal Transport and Planckian Claims supplies the experimental claims and extraction choices. Diffusion, Conductivity, and Susceptibility separates a diffusion time from a conductivity relaxation time.

Helpful background. Metallic Non-Fermi Liquids and Quasiparticle Breakdown shows why a quasiparticle lifetime may not exist; Linearized Kinetics and Relaxation Modes identifies mode-dependent decay rates; and Holographic Diffusion, Conductivity, and Momentum Relaxation provides solvable strongly coupled examples with explicit translation breaking.

Four inequivalent Planckian claims

Write an extracted rate as

$$\frac{1}{\tau_X}=\alpha_X\frac{k_B T}{\hbar}.$$

The subscript $X$ is essential. It may denote a Drude transport rate, a single-particle width, an energy-relaxation rate, an eigenvalue of a collision operator, a diffusion time $D/v^2$, or a many-body scrambling time. Even in one material these need not coincide. The distinction between an observable-specific rate and a conjectured common thermal scale is central to the modern synthesis Hartnoll and Mackenzie 2022, rate definitions and phenomenology.

Claim	Testable content	Present assessment
Universal lower bound $\tau_X\geq C\tau_{\mathrm P}$	A specified $X$, coefficient $C$, and theory class admit no counterexample	Not established; broad versions have counterexamples.
Quantum-critical scaling	With temperature the only infrared energy scale, a selected response has $\omega/T$ scaling and rate proportional to $T$	Established in some models and datasets, not universal across observables.
Transport parametrization	A Drude or memory-matrix analysis maps a $T$-linear resistivity slope to $\alpha_{\rm tr}=O(1)$	Empirically useful when band, density, and anisotropy uncertainties are carried through.
Phenomenological pattern	Many dissimilar metals yield order-one coefficients after conventional normalizations	Well documented, mechanistically underdetermined.

Scope-qualified conclusion. Planckian dissipation is best treated as an observable-specific scaling pattern and research constraint. It is not currently a universal bound on all relaxation, nor does $T$-linear resistivity alone establish a quantum-critical mechanism.

What is established

Several metal families show remarkably linear resistivity and inferred scattering rates of order $k_BT/\hbar$. A cross-material comparison made that pattern explicit Bruin et al. 2013. In overdoped cuprates, matched slopes across electron- and hole-doped systems support a common scale Legros et al. 2019. Angle-dependent magnetoresistance in Nd-LSCO further isolated an approximately isotropic $T$-linear rate with reported $\alpha=1.2\pm0.4$ under its Boltzmann and Fermi-surface analysis Grissonnanche et al. 2021.

These are experimental results about particular response models. The conversion

$$\rho=\frac{m^*}{n e^2\tau_{\rm tr}}$$

requires an effective mass, carrier density, current vertex, and usually a single-rate approximation. In multiband or anisotropic systems, the inferred $\tau_{\rm tr}$ is a weighted inverse response, not a directly timed microscopic event.

Assumptions and competing interpretations

Interpretation	Strongest evidence for it	Evidence against or limitation
A fundamental quantum speed limit controls transport.	Order-one rates recur in correlated materials; some solvable strongly coupled models relate diffusion, chaos, and thermal scales.	No general theorem maps uncertainty-time heuristics or chaos bounds to dc transport. A published electron-doped-cuprate analysis gives a counterexample to a proposed transport bound. Poniatowski et al. 2021
Scale invariance at a quantum critical point forces $T$-linear relaxation.	$T$ may be the only scale and $\omega/T$ response can follow.	Momentum conservation, dangerously irrelevant operators, disorder, density, and current overlap still control conductivity; not every quantum-critical observable has one rate.
Ordinary incoherent scattering saturates a stability ceiling.	Conventional metals and electron–phonon systems also cluster near the scale; a lattice-stability analysis explains a bound on a class of conventional $T$-linear resistivities. Mousatov and Hartnoll 2023	Quasielastic phonon scattering is not a many-body equilibration clock, so numerical similarity does not imply a shared Planckian mechanism.
“Planckian” is only dimensional analysis.	Any scale-invariant finite-temperature problem naturally contains $k_BT/\hbar$.	Repeated order-one coefficients and systematic doping/angle dependence are nontrivial empirical facts that still demand an explanation.

The strongest synthesis is therefore layered: the scaling can be real, the coefficient can be informative, and the universal-bound interpretation can still be false.

Negative results and uncertainty

• A $T$-linear resistivity can arise from high-temperature electron–phonon scattering, classical fluctuations, disorder-assisted mechanisms, or sums of channels. It is not a unique strange-metal diagnostic.
• Matthiessen-rule decompositions can move slope between “elastic” and “inelastic” pieces; extrapolating a residual intercept changes $\alpha$.
• Optical, dc, thermal, and single-particle rates use different vertices and frequency limits. Agreement within a factor of two is not an equality without a shared response calculation.
• Bad metals need not possess long-lived quasiparticles, so assigning $m^*$ and $\tau$ from a Drude form may be a parametrization rather than a microscopic lifetime.
• Holographic models can realize both order-one and parametrically modified transport depending on translation breaking and charge sector. Their variety tests conjectures; it does not by itself identify a material mechanism.

What would resolve the meaning?

A genuine bound requires a theorem with: the exact decay functional; the class of Hamiltonians and states; conserved quantities and momentum relaxation; the constant and allowed corrections; and saturation examples. One clean counterexample inside that class refutes it.

A mechanism claim requires simultaneous prediction of dc slope, optical line shape, angular dependence, thermal transport, and single-particle response from one microscopic model with independently measured band parameters. A scaling claim should demonstrate a common $\omega/T$ function over a widening window and specify crossover scales. Experiments that extract two inequivalent rates in the same sample are especially discriminating.

Connected methods and tests

• Quantum Matter and Emergence organizes the material and critical regimes; Thermal and Nonequilibrium Field Theory supplies response and relaxation language.
• Real-Time QFT, Kinetic Theory, and Hydrodynamics compares rate definitions and conservation laws.
• Evidence for Planckian Dissipation isolates the experimental extraction chain.
• Transport claims should be refit across temperature windows, background subtractions, dynamical exponents, and competing relaxation channels to expose false scaling collapse. Complexity or operator-growth proxies are not transport benchmarks and should not be used to identify a Planckian rate without an independently derived relation to the measured response function.

Evidence boundary

The finite source set includes primary transport measurements, a direct counterexample, a conventional-metal mechanism result, and one synthesis used only to organize rate definitions. Targeted searches of APS, Nature, Science, arXiv, and journal records covered public material through 11 August 2026. Reported coefficients were not recombined across incompatible Drude conventions, and the selection is not exhaustive.

References

• Bruin, J. A. N., Sakai, H., Perry, R. S., and Mackenzie, A. P. (2013). “Similarity of Scattering Rates in Metals Showing $T$-Linear Resistivity.” Science 339, 804–807. DOI.
• Grissonnanche, G., et al. (2021). “Linear-in Temperature Resistivity from an Isotropic Planckian Scattering Rate.” Nature 595, 667–672. DOI.
• Hartnoll, S. A., and Mackenzie, A. P. (2022). “Colloquium: Planckian Dissipation in Metals.” Reviews of Modern Physics 94, 041002. DOI.
• Legros, A., et al. (2019). “Universal $T$-Linear Resistivity and Planckian Dissipation in Overdoped Cuprates.” Nature Physics 15, 142–147. DOI.
• Mousatov, C. H., and Hartnoll, S. A. (2023). “A Stability Bound on the $T$-Linear Resistivity of Conventional Metals.” Proceedings of the National Academy of Sciences 120, e2208749120. DOI.
• Poniatowski, N. R., Sarkar, T., Lobo, R. P. S. M., Das Sarma, S., and Greene, R. L. (2021). “Counterexample to the Conjectured Planckian Bound on Transport.” Physical Review B 104, 235138. DOI.