The Generalized Master Equation and its Applications

Abstract

The generalized master equation (GME) is an entity one meets with on the wayside in one’s journey from the microscopic to the macroscopic level of the dynamics of large systems in statistical mechanics. The prominent character in this journey is not the GME but is the Pauli master equation (PME) also known as the Master equation. The latter, with its distinctive tendencies as are evident in the H-theorem and its generally built-in irreversibility, possesses the ability to guide the weary [1] traveller safely (?) to the realm of macroscopic phenomena. The importance of the GME is therefore not always appreciated in the normal course of this journey. In fact, usually, the equation is not even allowed to live long. Almost immediately after one makes its acquaintance, a procedure known as the Markoffian approximation [2] is thrust into the GME, destroying its special characteristics and converting it into the sought-after PME. There are, However, researchers, who admire the GME for its own qualities (and not merely for its ability to give birth to the PME), who have recently studied it in its own right and have put to use its potentialities.