Detecting the changes of wood properties with respect to elapsed years since wood formation by the eigenvalue distribution of near infrared spectral matrices

Abstract

Abstract The effects of aging on wood properties are usually evaluated based on cambial age, with the assumption that the properties do not change once the wood has formed. This study examined changes in wood properties with the number of years elapsed since wood formation. Near-infrared (NIR) spectra were acquired from various positions of 20 sample trees, and changes in the spectra were examined with respect to elapsed years. We considered changes in multiple traits inclusively, rather than individually, using the distribution of eigenvalues calculated from NIR spectral matrices. The diffusion of eigenvalues with an increase in elapsed years followed Dyson’s Brownian motion. The gradual increase in the first eigenvalue, which is equivalent to the Helmholtz-free energy, indicates that the xylem in the heartwood changes to a more ordered physical state over time. The variations in Shannon entropy and density matrix with elapsed years revealed the irreversibility of the aging process. The proposed method is independent of a specific coordinate system and can, therefore, be applied using a wide variety of information other than that obtained from NIR spectra.

Keywords

• Dyson’s Brownian motion
• Fokker–Planck equation
• Helmholtz-free energy
• Entropy
• Irreversible process