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arXiv:2602.04953

Information, Dissipation, and Planckian Optimality

Debanjan Chowdhury

cond-mat.str-elcond-mat.stat-mechquant-phSubmitted Feb 4, 2026• Announced Feb 6, 2026• 0 citations
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Abstract

We derive a universal bound on the efficiency with which "dissipated" work can generate distinguishable changes in a quantum many-body state at a finite temperature, as quantified by the quantum Fisher information. The bound follows solely from the analytic structure of equilibrium many-body correlators and is independent of all microscopic details. It takes a frequency-resolved form with a characteristic crossover at the Planckian scale, $ω_\star\sim k_B T/\hbar$. We find that Planckian scatterers sit at the edge of optimality, displaying maximal relaxation rate before information-dissipation efficiency collapses. This suggests strange metals are not just fast dissipators, but the fastest that remain efficient in generating distinguishability. The bounded quantity can be evaluated directly from optical conductivity measurements in strongly correlated electronic systems, offering a unique window into how dissipation generates distinguishable changes.

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6.5 pages, 1 figure

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We derive a universal bound on the efficiency with which "dissipated" work can generate distinguishable changes in a quantum many-body state at a finite temperature, as quantified by the quantum Fisher information. The bound follows solely from the analytic structure of equilibrium many-body correlators and is independent of all microscopic details. It takes a frequency-resolved form with a characteristic crossover at the Planckian scale, ω⋆∼kBT/ℏω_\star\sim k_B T/\hbarω⋆​∼kB​T/ℏ. We find that Planckian scatterers sit at the edge of optimality, displaying maximal relaxation rate before information-dissipation efficiency collapses. This suggests strange metals are not just fast dissipators, but the fastest that remain efficient in generating distinguishability. The bounded quantity can be evaluated directly from optical conductivity measurements in strongly correlated electronic systems, offering a unique window into how dissipation generates distinguishable changes.
The observation of Planckian scattering, often inferred from Drude fits in strongly correlated metals, raises the question of how to extract an intrinsic timescale from measurable quantities in a model-independent way. We address this by focusing on a ratio (B{\cal{B}}B) of spectral moments of the dissipative part of the optical conductivity and prove a rigorous upper bound on B{\cal{B}}B in terms of the Planckian rate. The bound emerges from the analytic structure of thermally weighted response functions of the current operator. Crucially, the bounded quantity is directly accessible via optical spectroscopy and computable from imaginary-time correlators in quantum Monte Carlo simulations, without any need for analytic continuation. We evaluate B{\cal{B}}B for simplified examples of both Drude and non-Drude forms of the optical conductivity with a single scattering rate in various asymptotic regimes, and find that B{\cal{B}}B lies far below the saturation value. These findings demonstrate that Planckian bounds can arise from fundamental constraints on equilibrium dynamics, pointing toward a possibly universal structure governing transport in correlated quantum matter.
The recent mathematical derivation by Abiuso et al. establishes a universal lower bound on quantum thermalization times, τth ≥ τPl /2 = ℏ/(2kB T ), utilizing quantum Fisher information geometry, Bures metric angles, and Hamiltonian estimation limits. While their operational result is mathematically exact, their underlying method relies on an adversarial epistemic formulation—treating thermalization as an information-acquisition game in which an external device or bath must “learn” or “estimate” the system Hamiltonian across a continuous family of operators. Decades of empirical and theoretical physics preceding this proof, from Zaanen’s identification of universal Planckian scattering in cuprate superconductors to Bruin and Mackenzie’s transport scaling across strange metals, alongside the Maldacena-Shenker-Stanford chaos bound and hydrodynamic fluctuation limits by Lucas and Delacrétaz, demonstrate that the Planckian scale is an objective physical feature of interacting systems rather than an artifact of measurement. In this work, we demonstrate that this bound does not arise because an open system requires time to resolve operator distinguishability. Rather, it is the direct mechanical consequence of physical metric work executed against positive manifold impedance in a ten-dimensional self-dual product manifold M3 × (T5 × S5 ). Within this geometry, physical time is a derived parameter (Virtual Time, T ) tracking the accumulation of metric work across an anisotropic 5-Space basis (α, x, y, z, Ω) mediated across the O(5, 5) T-duality boundary (R ↔ 1/R) by non-refundable Planck-floor transfer operations (∆E = ℏωP ). Under this strict zero-debt ledger, instantaneous collisional state swaps are topologically barred. At high temperatures (β∆ ≤ 1), the maximum rate of metric phase-slip across conjugate boundary cycles cannot exceed the energetic throughput permitted by the positive manifold impedance Ω ≥ 0, directly yielding τth ≥ ℏ/(2kB T ). In the low-temperature limit (β∆ ≫ 1), topological strain equilibrium (∆F → 0) halts Virtual Time (∂/∂T → 0), recovering the adiabatic quantum floor τ ≥ ℏ/∆ and guaranteeing vanishing decay widths (Γ ≡ 0). We salute the mathematical achievement of Abiuso et al. while demonstrating that the Planckian bound is an immutable elastodynamic property of spacetime rather than an epistemic limit of quantum estimation theory.
Relaxational processes for conduction electrons in metals come with characteristic temperature dependences; classic examples at low temperatures are the 1/T21/{T}^{2}1/T2 law for the relaxation time in a Fermi liquid, and the Bloch 1/T51/{T}^{5}1/T5 law for electron-phonon scattering. The strange metal phase of cuprate superconductors is governed instead by the Planckian time, which is given in terms of fundamental constants only. This Colloquium discusses the concept of such a fundamental timescale and the degree to which it provides a lower bound for relaxation times, and illustrates these ideas with examples from conventional and unconventional metals.
The pursuit of macroscopic quantum coherence in strongly correlated electron systems is fundamentally limited by Planckian dissipation, a universal scattering rate that renders active-dynamic control thermodynamically untenable. This paper introduces “Quantum Architectonics,” a design paradigm that leverages passive structural intelligence to overcome this limit. We propose the “Signal-Worker” ontology to unify the physics of 2D Moiré materials and 3D bulk complex oxides (e.g., Cuprates). Central to our framework is the Lossless Complexity Index (LCI), a metric for architectural quality. We provide a first-principles derivation showing the LCI optimum is a universal constant, LCIopt=ln⁡(2π)≈1.83LCI_{opt} = \ln(2\pi) \approx 1.83LCIopt​=ln(2π)≈1.83, derived from the fundamental bound on quantum chaos. Our computational models, which approximate Non-Markovian dynamics, demonstrate that optimized “Phononic Scaffolds” can achieve significant coherence gains over memoryless systems. We further show that d-wave pairing symmetry in Cuprates imposes a geometric penalty on shielding efficiency compared to isotropic s-wave systems. This work establishes a rigorous, unified roadmap for engineering “owned coherence,” projecting a theoretical pathway toward stable quantum operation at 77K.
I explore a theory of transport and optical properties of strange metallic carriers in strongly correlated systems that follows from assuming that the diffusion constant has reached its quantum limit D=ℏ/m, and that such quantum carriers behave as distinguishable particles as they would in an electronic solid. These assumptions immediately lead to T-linear resistivities with apparent Planckian scattering rates and, extending to the frequency domain, to the stretched Drude peaks and ω/T scaling commonly observed in optical absorption experiments in strange metals. This behavior can be rationalized by observing that when the thermal de Broglie length λ_{dB} exceeds the mean-free path, the carrier motion can no longer be described in terms of random collisions of classical particles as assumed by Drude-Boltzmann theory and should be viewed instead as a sequence of projective measurements collapsing the wave function.
We establish an end-to-end theoretical framework and numerical validation for the dissipation of metastable bound energy states, connecting empirical engineering lifetime forecasting of primary chemical cells to fundamental non-equilibrium quantum-informational thermodynamics. We prove that the irreversible relaxation of stored free energy Delta F into a thermal reservoir at temperature T is governed by the Planckian dissipation timescale tau_P = hbar / (k_B T) and the dimensionless Landauer information capacity Phi_0 = Delta F / (k_B T). Utilizing stochastic Langevin integration across a saddle-node bifurcation normal form, we uncover a universal power-law divergence of voltage noise variance prior to system collapse with critical exponent gamma = 1/2: Var(V, t) ~ (t_death - t)^(-1/2), offering an exact, non-invasive early-warning precursor for catastrophic failure. Furthermore, by numerically solving the exact unitary Schrodinger equation for an 8-qubit non-integrable chaotic Heisenberg spin chain via the Loschmidt Echo protocol, we demonstrate that macroscopic thermodynamic irreversibility emerges from many-body quantum information scrambling (reaching 72.1% of the Page thermalization entropy), wherein a microscopic 5% Hamiltonian perturbation collapses time-reversal fidelity to 19.74%. The universal master equation is validated across 52 orders of magnitude in energy, spanning intracellular ATP metabolic pools, galvanic cells, and degenerate cooling white dwarfs.