  The application of a temperature gradient to an extended system generates an
electromotive force that induces an electric current in conductors and a
macroscopic polarization in insulators. The ratio of the electromotive force to
the temperature difference, usually referred to as the Seebeck coefficient, is
often computed using non-equilibrium techniques, such as non-equilibrium
molecular dynamics (NEMD). In this paper we argue that thermo-polarization
effects in insulating fluids can be conveniently treated by standard
equilibrium thermodynamics and devise a protocol, based on a combination of
equilibrium molecular dynamics and Bayesian inference methods, that allows one
to compute the Seebeck coefficient in these systems along with a rigorous
estimate of the resulting statistical accuracy. The application of our
methodology to liquid SPC/E water results in good agreement with previous
studies, based on more elaborate NEMD simulations, and in a more reliable
estimate of the statistical accuracy of the results.
