  The entropy of an electronic system offers important insights into the nature
of its quantum mechanical ground state. This is particularly valuable in cases
where the state is difficult to identify by conventional experimental probes,
such as conductance. Traditionally, entropy measurements are based on bulk
properties, such as heat capacity, that are easily observed in macroscopic
samples but are unmeasurably small in systems that consist of only a few
particles. In this work, we develop a mesoscopic circuit to directly measure
the entropy of just a few electrons, and demonstrate its efficacy using the
well understood spin statistics of the first, second, and third electron ground
states in a GaAs quantum dot. The precision of this technique, quantifying the
entropy of a single spin-$\frac{1}{2}$ to within 5\% of the expected value of
$k_B \ln{2}$, shows its potential for probing more exotic systems. For example,
entangled states or those with non-Abelian statistics could be clearly
distinguished by their low-temperature entropy.
