  The thermodynamic definition of entropy can be extended to nonequilibrium
systems based on its relation to information. To apply this definition in
practice requires access to the physical system's microstates, which may be
prohibitively inefficient to sample or difficult to obtain experimentally. It
is beneficial, therefore, to relate the entropy to other integrated properties
which are accessible out of equilibrium. We focus on the structure factor,
which describes the spatial correlations of density fluctuations and can be
directly measured by scattering. The information gained by a given structure
factor regarding an otherwise unknown system provides an upper bound for the
system's entropy. We find that the maximum-entropy model corresponds to an
equilibrium system with an effective pair-interaction. Approximate closed-form
relations for the effective pair-potential and the resulting entropy in terms
of the structure factor are obtained. As examples, the relations are used to
estimate the entropy of an exactly solvable model and two simulated systems out
of equilibrium. The focus is on low-dimensional examples, where our method, as
well as a recently proposed compression-based one, can be tested against a
rigorous direct-sampling technique. The entropy inferred from the structure
factor is found to be consistent with the other methods, superior for larger
system sizes, and accurate in identifying global transitions. Our approach
allows for extensions of the theory to more complex systems and to higher-order
correlations.
