Stochastic thermodynamics extends classical thermodynamics to small systems
in contact with one or more heat baths. It can account for the effects of
thermal fluctuations and describe systems far from thermodynamic equilibrium. A
basic assumption is that the expression for Shannon entropy is the appropriate
description for the entropy of a nonequilibrium system in such a setting. Here,
for the first time, we measure experimentally this function. Our system is a
micron-scale colloidal particle in water, in a virtual double-well potential
created by a feedback trap. We measure the work to erase a fraction of a bit of
information and show that it is bounded by the Shannon entropy for a two-state
system. Further, by measuring directly the reversibility of slow protocols, we
can distinguish unambiguously between protocols that can and cannot reach the
expected thermodynamic bounds.Comment: 9 pages, 3 figures, and supplemental materia
