  Our aim is studying the thermodynamics of cosmological models including
initial and final de-Sitter eras. For this propose, bearing Cai-Kim temperature
in mind, we investigate the thermodynamic properties of a dark energy candidate
with variable energy density, and show that the state parameter of this dark
energy candidate should obey the $\omega_D\neq-1$ constraint, whiles there is
no interaction between the fluids filled the universe, and the universe is not
in the de-Sitter eras. Additionally, based on thermal fluctuation theory, we
study the possibility of inducing fluctuations to the entropy of the dark
energy candidate due to a mutual interaction between the cosmos sectors.
Therefore, we find a relation between the thermal fluctuations and the mutual
interaction between the cosmos sectors, whiles the dark energy candidate has a
varying energy density. We point to models in which a gravitationally induced
particle production process leads to change the expansion eras, whiles the
corresponding pressure is considered as the cause of current acceleration
phase. We study its thermodynamics, and show that such processes may also leave
thermal fluctuations into the system. We also find an expression between the
thermal fluctuations and the particle production rate. Finally, we use
Hayward-Kodama temperature to get a relation for the horizon entropy in models
including the gravitationally induced particle production process. Our study
shows that the first law of thermodynamics is available on the apparent horizon
whiles, the gravitationally induced particle production process, as the dark
energy candidate, may add an additional term to the Bekenstein limit of the
horizon.
