  Our Universe is expected to finally approach a de Sitter universe whose
horizon is considered to be in thermal equilibrium. In the present article,
both the energy stored on the horizon and its thermodynamic fluctuations are
examined through the holographic equipartition law. First, it is confirmed that
a flat Friedmann--Robertson--Walker universe approaches a de Sitter universe,
using a cosmological model close to lambda cold dark matter ($\Lambda$CDM)
models. Then, based on the holographic equipartition law, the energy density of
the Hubble volume is calculated from the energy on the Hubble horizon of a de
Sitter universe. The energy density for a de Sitter universe is constant and
the order of the energy density is consistent with the order of that for the
observed cosmological constant. Second, thermodynamic fluctuations of energy on
the horizon are examined, assuming stable fluctuations around thermal
equilibrium states. A standard formulation of the fluctuations for a canonical
ensemble is applied to the Hubble horizon of a de Sitter universe. The
thermodynamic fluctuations of the energy are found to be a universal constant
corresponding to the Planck energy, regardless of the Hubble parameter. In
contrast, the relative fluctuations of the energy can be characterized by the
ratio of the one-degree-of-freedom energy to the Planck energy. At the present
time, the order of the relative fluctuations should be within the range of a
discrepancy derived from a discussion of the cosmological constant problem,
namely a range approximately from $10^{-60}$ to $10^{-123}$. The present
results may imply that the energy stored on the Hubble horizon is related to a
kind of effective dark energy, whereas the energy that can be `maximally'
stored on the horizon may behave as if it were a kind of effective vacuum-like
energy in an extended holographic equipartition law.
