Physical limits to sensing material properties

All materials respond heterogeneously at small scales, which limits what a sensor can learn. Although previous studies have characterized measurement noise arising from thermal fluctuations, the limits imposed by structural heterogeneity have remained unclear. In this paper, we find that the least fractional uncertainty with which a sensor can determine a material constant λ₀ of an elastic medium is approximately δλ0/λ0~(Δλ1/2/λ0)(d/a)D/2(ξ/a)D/2 for a ≫ d ≫ ξ, λ0≫Δλ1/2, and D > 1, where a is the size of the sensor, d is its spatial resolution, ξ is the correlation length of fluctuations in λ₀, Δ_λ is the local variability of λ₀, and D is the dimension of the medium. Our results reveal how one can construct devices capable of sensing near these limits, e.g. for medical diagnostics. We use our theoretical framework to estimate the limits of mechanosensing in a biopolymer network, a sensory process involved in cellular behavior, medical diagnostics, and material fabrication.