  Motivated by the corrected form of the entropy-area law, and with the help of
von Neumann entropy of quantum matter, we construct an emergent spacetime by
the virtue of the geometric language of statistical information manifolds. We
discuss the link between Wald and Jacobson approaches of thermodynamic/gravity
correspondence and Fisher pseudo-Riemannian metric of information manifold. We
derive in detail Einstein's field equations in statistical information
geometric forms. This results in finding a quantum origin of a positive
cosmological constant that is founded on Fisher metric. This cosmological
constant resembles those found in Lovelock's theories in a de Sitter background
as a result of using the complex extension of spacetime and the Gaussian
exponential families of probability distributions, and we find a time varying
dynamical gravitational constant as a function of Fisher metric together with
the corresponding Ryu-Takayanagi formula of such system. Consequently, we
obtain a dynamical equation for the entropy in information manifold using
Liouville-von Neumann equation from the Hamiltonian of the system. This
Hamiltonian is suggested to be non-Hermitian, which corroborates the approaches
that relate non-unitary conformal field theories to information manifolds. This
provides some insights on resolving "the problem of time".
