A generalized dielectric polarization evolution equation

In this paper a non-equilibrium statistical-mechanical theory of dielectric relaxation is developed. This approach differs from previous work in that a generalized nonlocal evolution equation for the polarization is constructed. General equations of motion are presented for the polarization, internal energy, and entropy which include effects of memory. These equations can be expressed in terms of reduced-correlation functions, and are valid for non-equilibrium and arbitrary field strengths. Expressions for an effective local field also are developed. The Fourier transform of the evolution equation yields a general compact expression for the Fourier transform of the memory function and a specific form for the susceptibility. The kernel, Fourier transform of the memory function are developed, and relaxation-time functions for special cases. In the limit of a single relaxation time, a Debye response is obtained. In the subsequent special cases exponential and Gaussian forms for the memory functions are assumed. The final special case relates a power-law circuit transfer function to the theory of Dissado and Hill. In this case the memory kernel and relaxation times are derived from the Dissado-Hill response function.