This paper investigates modifications to the FLRW cosmology resulting from
considering general entropy for the cosmological apparent horizon. Although the
Bekenstein-Hawking entropy has been successful in the study of the
thermodynamics of black holes and cosmology, according to the laws of
thermodynamics, considering this entropy, it imposes a w=β1 limit on the
equation of state of the cosmic fluid. To address this limitation, Nojiri and
colleagues in 2022, introduced generalized entropies with four-parameters that
may tend to familiar entropies and can solve some problems of cosmology. In
this paper, we explore how correcting the entropy affects the Energy-momentum
tensor of the cosmic flux from the outset. Our calculations show that in any
way, the modified Bekenstein-Hawking entropy can be still considered as a
general entropy after a modification energy-momentum density tensor with a
correction function f(Ο). The function f(Ο) can be easily
reconstructed, by considering the thermodynamics of the apparent horizon. We
also study the first and second laws of thermodynamics in this context and show
how the problem of limited cosmic flux can be resolved based on the model's
parameters. At last, In order to study the kinematics of the universe,
cosmography parameters are also calculated and we see that the correction
function f(Ο) has a non-negligible role in cosmography parameters. This
paper provides valuable insights into using general entropies on the apparent
horizon of the universe.Comment: 12 page