Information, Dissipation, and Planckian Optimality

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.

Figures (1)

• Figure 1: Normalized information-dissipation efficiency kernel (solid blue curve), $\eta(\omega)/\beta$; see Eq. \ref{['eq:main_bound_intro']}. The shaded region indicates the approximate Planckian window where dissipation is maximally efficient. Three representative dissipative optical spectra are shown: a narrow Drude (purple dash-dotted), a Planckian Drude (green dashed), and a broad Drude (red dotted) peak, respectively. Systems with spectral weight concentrated in the Planckian window (shaded region) achieve near-optimal information-dissipation efficiency, while those with significant high-frequency weight are parametrically inefficient.