  D.J. Evans, et al., [Phys. Rev. Lett. 71, 2401 (1993)] discovered a relation,
subsequently known as the Fluctuation Theorem (FT), which quantifies the
probability of observing fluctuations violating the second law of
thermodynamics in thermostatted dissipative non-equilibrium systems. The FT has
been confirmed experimentally for small systems. We analyze fluctuations of the
total entropy production related to the distribution of the magnetic energy
density in the quiet Sun lower atmosphere inferred by means of
spectro-polarimetric observations. We show that the magnetic energy density is
intermittent, at non-equilibrium and has the Markov property. The applicability
of the FT is proven for the first time in an astronomical environment in spite
of the seemingly large scales involved. We also found a non-linear behavior of
the probability current, indicating that the dynamics of the magnetic field
depends on the field strength. On average, however, the observed
non-equilibrium behavior is governed by the second law of thermodynamics for
open systems. Our results provide novel constraints for testing the
hypothesizes of the solar local dynamo, which should be consistent with the
inferred statistics of the fluctuations.
