A novel computational scheme has been used to predict the electric potentials generated by arbitrary temperature gradients in semiconductor materials. Written in object-oriented code, the Discrete State Simulation (DSS) is a coupled cellular automata simulator that builds upon the objects and rules of quantum mechanics. The DSS represents global non-equilibrium processes as patterns that emerge through an ensemble of scattering events that are localized at vibronic nodes. By tracking the energy-momentum-position coordinates of the individual particles that define the vibronic state at a node, the DSS undercuts equilibrium concepts such as temperature. Consequently, the DSS can represent physical systems that are described by more than one temperature or that contain physical features that defy definitions of temperature. Using modified bootstrap sampling algorithms, the DSS depicted (1) shifts in distribution functions induced by external fields and temperature gradients, (2) field-dependent transitions from linear mobility to non-linear mobility, (3) saturation velocities, (4) non-exponential decay functions generated by multiple phonon scattering modes, and (5) charge separations and electric potentials generated by temperature gradients. Ensemble averages were sensitive to the structure of dispersion relations, to the energy of the system, and to quantum coupling strengths. Seebeck coefficients were sensitive to the features of the electronic and the vibrational band structures, and their associated coupling coefficients.