  In this paper, we aim to interpret the background gravitational effects
appearing in quantum field theory on curved space-time by studying the Brownian
motion of quantum states along with the Hamilton-Perelman Ricci flow. It has
been shown that the Wiener measure automatically contains the Einstein-Hilbert
action and the path-integral formulation of the scalar quantum field theory on
curved space-time at the first order of local approximations. This provides a
well-defined formulation of the path-integral measure for quantum field theory
in the presence of gravity. However, we establish that the emergence of
Einstein-Hilbert action is independent of the matter field interactions and is
a merely entropic/geometric effect stemming from the nature of the Ricci flow
of the universe geometry. We also extract an explicit formula for the
cosmological constant in terms of the Ricci flow and the Hamilton theorem for
3-manifolds. Then, we discuss the cosmological features of the FLRW solution in
the LambdaCDM Model via the derived equations of the Ricci flow. We also argue
the correlation between our formulations and the entropic aspects of gravity.
Finally, we provide some theoretical evidence that proves the second law of
thermodynamics is the basic source of gravity and probably a more fundamental
concept.
