Reverberation chamber as a statistical relaxation process: Entropy analysis and fast time domain simulations

In this contribution, we investigate the entropy growth in a mode-stirred cavity simulated by the FDTD method. The adopted reverberation chamber is efficiently stirred by multiple paddles and excited by a Gaussian pulse. It is observed that the entropy starts growing quadratically in time, then it increases linearly during the energy buildup, and it saturates after a few nanoseconds, when the full onset of chaotic regime is developed. This allows for terminating the numerical simulations well before the Richardson time, as the asymptotic entropy is rapidly achieved. The analysis is based on the eigenvalues of the correlation matrix, calculated over a dense grid of spatial points, thus supporting the perspective of the reverberation chamber as a statistical multivariate process. The number of orthogonal eigenvectors (principal components) can be estimated and used as the number of statistically independent stirrer positions (degrees of freedom, cavity realizations). It is found that letting the chamber evolve for a very long time would gain only a few principal components, thus adding a negligible improvement in the stirring performances. Different mode-stirrer shapes can be investigated and their efficiency quantified by this method.