The narrow escape problem (NEP) [1-4] is ubiquitous in physics, chemistry and biology. It deals with the calculation of the mean time it takes a Brownian particle inside a bounded domain to exit through a narrow escape window on the domain's boundary.

In the past two decades this beautiful and mathematically intricate problem has received much attention, as it was realized that the mean escape time controls the rates of many important processes in molecular and cellular biology.

In a host of situations of biological importance there are many particles present which attempt to escape through a small escape window. If these particles are treated as non-interacting Brownian particles, the escape statistics can be readily expressed via the one-particle statistics. Quite often, however, the particles interact with each other, such as in a highly crowded intracellular environment. Although the importance of interactions may have been recognized earlier, there have been no attempts to include them in the theory.

We developed a general formalism which allows to evaluate the escape statistics of an ensemble of many interacting diffusing particles [5]. The formalism is based on the fluctuating hydrodynamics and the recently developed macroscopic fluctuation theory [6]. This paradigm shift opens new perspectives for understanding diffusive transport through small holes in a host of applications.

[1] I.V. Grigoriev, Y.A. Makhnovskii, A.M. Berezhkovskii and V.Y. Zitserman, J. Chem. Phys. 116, 9574 (2002).

[2] P.C. Bressloff and J.M. Newby, Rev. Mod. Phys. 85, 135 (2013).

[3] O. Bénichou and R. Voituriez, Phys. Rep. 539, 225 (2014).

[4] D. Holcman and Z. Schuss, Stochastic Narrow Escape in Molecular and Cellular Biology (Springer, New York, 2015).

[5] T. Agranov and B. Meerson, arXiv:1711.02465

[6] L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim. Rev. Mod. Phys. 87, 593 (2015).