Author Correction: Thermodynamic uncertainty relations constrain non-equilibrium fluctuations

Correction to: Nature Physics https://doi.org/10.1038/s41567-019-0702-6, published online 11 November 2019.

In the version of this Perspective originally published, in Box 1, the sentence “The single particle in the high-energy site can move to the lower-energy site with rate p, but in doing so the system will lose energy ΔE.” has been amended to read “The single particle in the site with high energy E₁ can move to the site with lower energy E₂ with rate p, but in doing so the system will lose energy ΔE = E₁ − E₂.” Accordingly, also in Box 1, the following equation changes have been made. (1) In the equations for ‘ $\frac{\alpha }{\gamma }$ ’ and ‘$\frac{\beta }{\delta }$ ’, the superscripts ‘μ_left/k_BT’ and ‘−μ_rightk_BT’, respectively, should have been ‘(μ_left−E₁)/k_BT’ and ‘−(μ_right−E₂)/k_BT’; the correct equations are ‘$\frac{\alpha }{\gamma } = e^{\left( {\mu _{{\mathrm{left}}} - E_1} \right){\mathrm{/}}k_{\mathrm{B}}T}$’ and ‘$\frac{\beta }{\delta } = e^{ - \left( {\mu _{{\mathrm{right}}} - E_2} \right){\mathrm{/}}k_{\mathrm{B}}T}$’. (2) In the equation in the sentence beginning “For example:”, the term ‘$+ \frac{{\Delta E}}{{k_{\mathrm{B}}T}}$’ should not have been included; the correct equation is:

The online versions of the Perspective have been amended.