  A symmetry breaking (SB) involves an abrupt change in the set of microstates
that a system can explore. This change has unavoidable thermodynamic
implications. According to Boltzmann's microscopic interpretation of entropy, a
shrinkage of the set of compatible states implies a decrease of entropy, which
eventually needs to be compensated by dissipation of heat and consequently
requires work. Examples are the compression of a gas and the erasure of
information. On the other hand, in a spontaneous SB, the available phase space
volume changes without the need for work, yielding an apparent decrease of
entropy. Here we show that this decrease of entropy is a key ingredient in the
Szilard engine and Landauer's principle and report on a direct measurement of
the entropy change along SB transitions in a Brownian particle. The SB is
induced by a bistable potential created with two optical traps. The experiment
confirms theoretical results based on fluctuation theorems, allows us to
reproduce the Szilard engine extracting energy from a single thermal bath, and
shows that the signature of a SB in the energetics is measurable, providing new
methods to detect, for example, the coexistence of metastable states in
macromolecules.
