The application of a temperature gradient to an extended system generates an electromotive force that induces an electric current in conductors and 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 nonequilibrium techniques, such as nonequilibrium molecular dynamics (NEMD). In this article, 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.
E. Drigo and S. Baroni, Seebeck Coefficient of Liquid Water from Equilibrium Molecular Dynamics, J. Chem. Theory Comput. 2023, 19, 23, 8855–8860 (2023).