  A pair of Majorana zero modes (MZMs) constitutes a nonlocal qubit whose
entropy is $\log 2$. Upon strongly coupling one of the constituent MZMs to a
reservoir with a continuous density of states, a universal entropy change of
$\frac{1}{2}\log 2$ is expected to be observed across an intermediate
temperature plateau. We adapt the entropy-measurement scheme that was the basis
of a recent experiment [Hartman et. al., Nat. Phys. 14, 1083 (2018)] to the
case of a proximitized topological system hosting MZMs, and propose a method to
measure this $\frac{1}{2}\log 2$ entropy change --- an unambiguous signature of
the nonlocal nature of the topological state. This approach offers an
experimental strategy to distinguish MZMs from non-topological states.
