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We extend the linear response-like derivation of the generalized Navier-Stokes equation to non-Newtonian flows with rate of strain-dependent transport coefficients. We derive a time correlation function expression for the viscosity tensor and point out possible ambiguities in the operational definitions of viscosity coefficients. Our analysis is specific to a suspension of polar, rod-like ferromagnetic particles. A commentary is included about the approximations that lead from the time correlation function and the molecular definition of the viscosity tensor to the standard, Brownian dynamics model used in the theoretical rheology of suspensions. Some theoretical difficulties and logical inconsistencies are pointed out. Preliminary results for the transport coefficients of dilute suspension of magnetic rod-like particles are presented.

An extension of the linear transport laws is derived from first principles of statistical mechanics. The resulting transport laws include both relaxation and nonlinear terms. It is found when these terms are included the Onsager reciprocal relations are no longer valid. Therefore, the development gives the limit of validity of the Onsager relations, as well as expressing the transport coefficients as correlation functions of the dynamical variables. In order to show the validity of the procedure used, a functional integral is derived as a first-order approximation for the transition probability. This integral when evaluated verifies the assumption of Onsager and Machlup for the transition probability for the linear transport laws.

A new derivation is presented of the properties of the travelling wave phase factors which are important in the semi-classical theory of high energy charge exchange processes. In the case of a rectilinear, constant velocity trajectory the phases obtained are those required by the Galilean invariance of the non-relativistic Schrodinger operator. For an arbitrary trajectory this invariance is not maintained and so there appear in the Schrodinger operator compensating terms which cannot be transformed away by a change of phase.

The memory function formulation of the time‐dependent Schrodinger equation is used to analyze the internal state problem associated with the decoupled motions or impact parameter approximation to binary collisional events. The exact, time‐orderd memory functions are then replaced with their time‐disordered counterparts. This generates a unitary approximation to the collision problem as well as simple, easily interpretable formulas for the transition probabilities. Two specific examples are considered in detail, namely, (i) the three‐state resonant transfer model and (ii) a ’’paired‐states’’ model for the dynamics of a many‐state problem.

Using the interaction picture, formal time dependent solutions of the Zwanzig-Feshbach projection operator method are derived which involve a nonunitary time-ordered memory operator. The familiar approximation which leads to a decoupling of the translational and internal motions in terms of a classical trajectory is derived by a systematic procedure which emphasises the generators of observable (operator) motion rather than the generators of wavefunction motion. Two-state approximations to this decoupled system are considered. These depend upon different approximations to the memory operator. Neglect of the memory operator together with the use of the stationary phase method produces the Landau-Zener approximation. Two extensions of this approximation are considered which depend upon different time disordered approximations to the two-state memory operator. Treating the continuum as a single state gives the bound-to-continuum analogues of these approximations.

General formulas have been derived for the molecular friction coefficients of a dilute gas. The velocity and temperature dependencies of these coefficients are examined in detail for several choices of the pair interaction potential. Also we have considered the frictional loss of kinetic energy and, for one special case, the dissipation of molecular internal angular momentum. The concepts of free path length and collision frequency are extended to nonrigid molecular models.

The equations of change for the statistical distribution functions involved in the kinetic theory are examined for molecular species which interact with arbitrary central forces. It is shown that the notion of inverse encounters follows in a straightforward fashion from the fundamental Liouville equation. The analysis also establishes that it is not the usual singlet distribution function, but a particular modification thereof, which should satisfy an equation of the Boltzmann variety. Three body collision processes are briefly examined and the extension of the method to the domain of chemical kinetics discussed.

Classical continuum theory is generalized to provide a systematic procedure for treating in successively greater detail the macroscopic manifestations of subcontinuum events without sacrificing the convenience of the field approach. The point of departure from traditional theory is the general angular momentum principle for continua. Internal angular momentum is associated with configurational and kinematic structure of the continuum ‘particle' and that structure is represented by moment expansions in polyadic polarization densities. Each step in the theoretical development is analyzed both in terms of the statistical mechanics of polyatomic media and from the standpoint of continuum physics. Accurate accounting of content and flux is found to require introducing the concepts of proper densities and currents. Among topics examined in detail are asymmetric states of stress, equations of change for dynamical variables, and equilibrium conditions in structured continua, including alinement of internal angular momentum with the principle axes of local mass distributions.

The methods of Prigogine and Resibois are used to construct a description of classical two‐body scattering events which bears a close formal analogy to that of time‐dependent quantum‐scattering theory. It is shown how the distribution in phase space evolves after long times into a steady‐state scattering form, from which expressions for cross sections and transition rates are obtained by means similar to those of the quantum‐mechanical treatment. These expressions are shown to be equivalent to the conventional classical formulas but offer in principle alternative means of evaluation.