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 . This relation itself is of independent interest, with applications not only to cellular chemosensation, but also to the reliability of other biological processes, like clocks and motors, as a function of energy consumption .
After 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 .