  Energy transfer (relaxation) phenomena are ubiquitous in nature. At a
macroscopic level, the phenomenological theory of heat (Fourier law)
successfully describes heat transfer and energy flow. However, its microscopic
origin is still under debate. This is because the phenomena can contain
many-body, multi-scale, nonequilibrium, and even quantum mechanical aspects,
which present significant challenges to theories addressing energy transfer
phenomena in physics, chemistry and biology. In this paper, we describe our
recent theoretical attempts to treat vibrational energy relaxation (VER) in
biomolecular systems, including peptide, porphyrin, and protein. First we
construct a reduced model using (instantaneous) normal mode analysis, and
further add anharmonic coupling between vibrational modes. Using such a model
combined with time-dependent perturbation theory for the anharmonic coupling,
we derive non-Markovian VER formulas, which are applicable to small timescales
such as sub picoseconds. We apply the VER formulas with full atomistic detail
to various biomolecular systems, discuss the VER timescales and mechanisms, and
compare with experiment if possible. We finally mention further theoretical
prospects of the energy transfer phenomena in physics, chemistry, and biology.
