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We formulate the statistical mechanical description of liquid systems forboth polarizable and polar systems in an electric field in the$\mathbf{E}$-ensemble, which is the pendant to the thermodynamic description interms of the free energy at constant potential. The contribution of theelectric field to the configurational integral $\tilde{Q}_{N}(\mathbf{E})$ inthe $\mathbf{E}$-ensemble is given in an exact form as a factor in theintegrand of $\tilde{Q}_{N}(\mathbf{E})$. We calculate the contribution of theelectric field to the Ornstein-Zernike formula for the scattering function inthe $\mathbf{E}$-ensemble. As an application we determine the field inducedshift of the critical temperature for polarizable and polar liquids, and showthat the shift is upward for polarizable liquids and downward for polarliquids.

Statistical mechanical description of liquid systems in electric field