  It is assumed that the spacetime is composed by events and can be explained
by partially ordered set (causal set). The parent events born two kinds of
children. Some children have a causal relation with their parents and other
kinds have not. It is assumed that evolution of the population is only happen
by the causal children. The assumed population can be modeled by finite
(infinite) dimension Leslie matrix. In both finite and infinite cases, it is
shown that the stationary state of the population always exists and the matrix
has positive eigenvalues. By finding the relation between the statistical
information of the population and the stationary state, a probability matrix
and a Shannon-like entropy is defined. It is shown that the change in entropy
is always quantized and positive and in consequence, the world is inflating. We
show that the vacuum energy can be attributed to the necessary done work for
preserving the causal relation between the parents and the children (cohesive
energy). By assuming that the sum of cohesive energy and kinetic energy of the
denumerable causal spacetime is equal to the heat, which flows across a causal
horizon, we find the relation between energy-momentum tensor and discrete Ricci
tensor which can be called the Einstein state equation. Finally, it is shown
that the constant of proportionality \(\eta\) between the entropy and the area
is proportional to \(\frac{k_{B}}{l_{p}^{2}}\) at Planck scale which is in good
agreement with the Hawking's result.
