The path probability method of irreversible statistical mechanics is reviewed and is applied to diffusion and relaxation processes in cooperative systems. Parts of previous reports by the author are corrected and expanded. In Part I it is shown that the irreversible case can be formulated by adding a space axis to the equilibrium statistical mechanics, and that the most probable path in time taken by the system is derived by maximizing the path probability. Two kinds of interaction with the heat bath are pointed out and a new formulation for the activated process is introduced. In Part II atomic diffusion in crystals, assuming the vacancy mechanism, is discussed. Using the new interpretation of the activation process, Reiss's result for one dimension is confirmed. The diffusion coefficient is derived for a general binary solid solution, and special cases are discussed. The concept of the diffusion activity introduced by Reiss does simplify the diffusion coefficient for a one-component system in three dimension, but not for a binary system. A simple interpretation of the formula for the path variables is presented, and the implicit use of a superposition approximation is pointed out. In Part III relaxation processes of cooperative systems are discussed. An inhomogeneous one-dimensional Ising model is treated as an example. A binary order-disorder system (of 50-50 composition) is discussed using the vacancy mechanism of atomic migration. The relaxation times of the order parameters are derived for the homogeneous phase.