Evaluation of the age dependent variation of wood properties based on the eigenvalue distribution of near infrared spectral matrices

Abstract

The age-dependent variation in wood properties is a very complex phenomenon because its pattern is highly dependent on tree species and wood traits. In this study, we evaluated the variation of multiple traits inclusively based on the distribution of eigenvalues calculated from the near-infrared spectral matrix at each cambial age. The experiments were conducted on four tree species with characteristic xylem structures, aiming to clarify the intrinsic behaviour of tree aging independent of tree species. The eigenvalues diffused with age in any species, such as in Dyson's Brownian motion. The gradual increase in the first eigenvalue, which is equivalent to the Helmholtz free energy, indicates that trees form a more ordered wood with age. As all the variations induced by various wood properties during the process of tree growth were aggregated into the set of eigenvalues, the Fokker-Planck equation representing the variation of eigenvalue distribution might provide a conclusive answer for the determination of demarcation between juvenile and mature wood. The age dependency of Shannon entropy and density matrix calculated from the probability associated with each energy eigenstate provided us with knowledge from the perspective of randomness; namely, tree aging from the perspective of the variation of wood properties was clearly an irreversible process. This result offers an important clue for sustainable forest management and the use of wood resources. The proposed method does not depend on a specific coordinate, thus, it will work well using data other than the near infrared spectrum.