Before revision:  Our derivations generalize the classic 1977 Berg-Purcell limit on cellular chemosensation along multiple dimensions, and also yield a novel thermodynamic uncertainty relation for the time a physical system spends in a pool of states .
After revision:  Our results generalize the classic 1977 Berg-Purcell limit on cellular chemosensation along multiple dimensions, and also yield a novel thermodynamic uncertainty relation for the time a physical system spends in a pool of states .