Evidence for Planckian Dissipation

Many metals with $T$ -linear resistivity yield an inferred relaxation rate of order $k_B T/\hbar$ . The recurrence is a useful empirical scaling clue, not evidence for a universal microscopic clock or a proved upper bound: the dimensionless coefficient depends on which lifetime is extracted, on the transport model, and on material parameters that can share large systematic errors.

Evidence cutoff. 11 August 2026. Reassess by 11 February 2027 or when frequency-resolved transport, a new or parametrically controlled counterexample, or a theorem materially changes the interpretation.

Required background. Strange-metal transport and Planckian scaling defines the empirical proposal; diffusion, conductivity, and susceptibility distinguishes measured response from an inferred relaxation time.

Helpful background. Quantum-critical non-Fermi liquids supplies competing mechanisms; linearized kinetic relaxation modes explains when a single $\tau$ is meaningful; criticality evidence and model discrimination prevents scaling collapse from being treated as a unique mechanism.

The rate being inferred

A common parameterization is

\frac{\hbar}{\tau}=\alpha k_B T,

with “Planckian” often meaning $\alpha$ of order unity. In a one-component Drude interpretation,

\rho(T)=\frac{m^*}{n e^2\tau(T)}

turns the slope of a linear resistivity into $\alpha$ . This requires a carrier density $n$ , an effective mass $m^*$ , and a single transport lifetime. Strongly correlated or multiband metals need not satisfy those assumptions, and a quasiparticle decay time, optical transport time, diffusion time, and many-body equilibration time need not coincide.

The bounded claim is therefore empirical: do published rates, extracted with declared procedures, cluster near $k_BT/\hbar$ ? The stronger claim of a universal bound or mechanism is assessed separately.

Evidence matrix

Source and method	Relation to the bounded claim	Independence	Result and stated uncertainty	Main limitation
Bruin et al., 2013, Drude conversion across several metals	supports order-one clustering	reanalysis of heterogeneous published data; material experiments are distinct but extraction assumptions are shared	scattering-rate slopes are similar to $k_B/\hbar$ within order-one factors	masses, densities, and the validity of one- $\tau$ transport are not uniformly controlled
Legros et al., 2019, overdoped cuprate resistivity and quantum oscillation inputs	supports a near-universal linear coefficient within the studied cuprates	several compounds and dopings; shared analysis framework and related material family	$T$ -linear resistivity maps to an order-one Planckian coefficient	mass and carrier-density assignments change across the phase diagram and can correlate with the inferred rate
Cao et al., 2020, magic-angle graphene	supports recurrence in a tunable, microscopically different platform	distinct material and device; still uses a Drude-like rate extraction	broad filling range with linear resistivity and a near-Planckian inferred rate	twist-angle inhomogeneity, narrow-band parameters, and non-Drude transport complicate $\tau$
Poniatowski et al., 2021, overdoped electron-doped cuprate transport	directly challenges a conjectured upper bound on an inferred transport rate	a different cuprate family and phenomenological analysis; still relies on converting dc transport to a lifetime	the reported transport phenomenology exceeds the proposed Planckian bound within the declared extraction	it is a counterexample to that transport-bound formulation, not to every Planckian time or local-equilibration conjecture
Conventional metals included in Bruin et al., 2013 and reviewed by Hartnoll and Mackenzie, 2022	qualifies the claim that Planckian scaling uniquely diagnoses strange-metal quantum criticality	different microscopic scattering mechanism, notably phonons	order- $k_BT/\hbar$ rates can occur outside strange-metal regimes	high-temperature quasiparticle and saturation physics differs by material; similarity is dimensional, not necessarily dynamical
Hartnoll and Mackenzie, 2022, critical review of lifetimes and bounds	evidence against an unqualified universal interpretation	synthesis rather than an independent experiment	distinguishes transport, quasiparticle, and many-body times; finds no single inference establishes a universal bound	conclusions depend on a diverse and sometimes incomplete experimental record

Supported pattern, unsupported theorem

The cross-material recurrence is real enough to demand explanation. It survives changes of dimensionality, carrier type, and microscopic setting, and in some materials the same order-one coefficient persists over a broad tuning range. But “order one” is intrinsically coarse. An uncertain factor in $m^*/n$ , parallel conductivity, or current-vertex corrections can move $\alpha$ across the proposed boundary without changing the measured resistivity.

The observation $\rho\propto T$ is weaker still. Dimensional analysis near a scale-invariant regime makes $k_BT/\hbar$ a natural rate, while electron–phonon scattering can also generate a linear resistivity and a comparable extracted rate. Thus the scale does not identify the scattering channel, prove the absence of quasiparticles, or establish quantum criticality.

The overdoped electron-doped cuprate analysis directly contradicts one proposed upper bound on the operational transport rate extracted there. It does not establish the reverse inequality for every definition of $\tau$ , nor does evidence in this set prove a universal local-equilibration bound. A proposed bound must specify the operator, state, frequency limit, extraction, and numerical coefficient; otherwise switching among inequivalent relaxation times changes the proposition.

What would change the assessment

The universal-clock interpretation would strengthen if dc, optical, thermal, and spectroscopic measurements in the same samples converged on one rate after a controlled memory-matrix or kinetic analysis, with material parameters measured independently. A theorem connecting that operational rate to $T$ under stated locality and spectral assumptions would change the status from pattern to bound.

The interpretation would weaken if well-controlled multiband inversions systematically produced parametrically different coefficients, or if the observed linear resistivity were quantitatively explained by a conventional mechanism while the relevant microscopic relaxation time was not Planckian.

Source selection

The finite set includes the original broad comparison, a high-control hole-doped cuprate family, a tunable moiré platform, a direct electron-doped transport counterexample, and a critical synthesis that explicitly separates lifetimes and conventional mechanisms. Papers quoting “Planckian” solely from a linear slope without an independently justified conversion were not counted as independent evidence.

Planckian dissipation: what does it mean? for competing definitions and proposed bounds.
Quantum matter and emergence for neighboring strange-metal programs.
Schwinger–Keldysh, kinetic theory, and hydrodynamics for operational relaxation modes.

References

Bruin, J. A. N., H. Sakai, R. S. Perry, and A. P. Mackenzie. “Similarity of Scattering Rates in Metals Showing $T$ -Linear Resistivity.” Science 339 (2013): 804–807. DOI.
Cao, Yuan, et al. “Strange Metal in Magic-Angle Graphene with near Planckian Dissipation.” Physical Review Letters 124 (2020): 076801. DOI.
Hartnoll, Sean A., and Andrew P. Mackenzie. “Colloquium: Planckian Dissipation in Metals.” Reviews of Modern Physics 94 (2022): 041002. DOI.
Legros, A., et al. “Universal $T$ -Linear Resistivity and Planckian Dissipation in Overdoped Cuprates.” Nature Physics 15 (2019): 142–147. DOI.
Poniatowski, Nicholas R., Tarapada Sarkar, Ricardo P. S. M. Lobo, Sankar Das Sarma, and Richard L. Greene. “Counterexample to the Conjectured Planckian Bound on Transport.” Physical Review B 104 (2021): 235138. DOI.