We present a novel framework for rigid point cloud registration. Our approach is based on the principles of mechanics and thermodynamics. We solve the registration problem by assuming point clouds as rigid bodies consisting of particles. Forces can be applied between both particle systems so that they attract or repel each other. These forces are used to cause rigid-body motion of one particle system toward the other, until both are aligned. The framework supports physics-based registration processes with arbitrary driving forces, depending on the desired behaviour. Additionally, the approach handles feature-enhanced point clouds, e.g., by colours or intensity values. Our framework is freely accessible for download. In contrast to already existing algorithms, our contribution is to precisely register high-resolution point clouds with nearly constant computational effort and without the need for pre-processing, sub-sampling or pre-alignment. At the same time, the quality is up to 28 percent higher than for state-of-the-art algorithms and up to 49 percent higher when considering feature-enhanced point clouds. Even in the presence of noise, our registration approach is one of the most robust, on par with state-of-the-art implementations.