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 construct ed. General equations of motion are presented for the polarization, interna l energy, and entropy which include effects of memory. These equations can be expressed in terms of reduced-correlation functions, and are valid for n on-equilibrium and arbitrary field strengths. Expressions for an effective local field also are developed. The Fourier transform of the evolution equa tion yields a general compact expression for the Fourier transform of the m emory function and a specific form for the susceptibility. The kernel, Four ier transform of the memory function are developed, and relaxation-time fun ctions for special cases. In the limit of a single relaxation time, a Debye response is obtained. In the subsequent special cases exponential and Gaus sian forms for the memory functions are assumed. The final special case rel ates a power-law circuit transfer function to the theory of Dissado and Hil l. In this case the memory kernel and relaxation times are derived from the Dissado-Hill response function.