  Entropy is a fundamental thermodynamic quantity indicative of the accessible
degrees of freedom in a system. While it has been suggested that the entropy of
a mesoscopic system can yield nontrivial information on emergence of exotic
states, its measurement in such small electron-number system is a daunting
task. Here we propose a method to extract the entropy of a Coulomb-blockaded
mesoscopic system from transport measurements. We prove analytically and
demonstrate numerically the applicability of the method to such a mesoscopic
system of arbitrary spectrum and degeneracies. We then apply our procedure to
measurements of thermoelectric response of a single quantum dot, and
demonstrate how it can be used to deduce the entropy change across
Coulomb-blockade valleys, resolving, along the way, a long-standing puzzle of
the experimentally observed finite thermoelectric response at the apparent
particle-hole symmetric point.
