How much a galaxy knows about its large-scale environment?: An
  information theoretic perspective
  The small-scale environment characterized by the local density is known to
play a crucial role in deciding the galaxy properties but the role of
large-scale environment on galaxy formation and evolution still remain a less
clear issue. We propose an information theoretic framework to investigate the
influence of large-scale environment on galaxy properties and apply it to the
data from the Galaxy Zoo project which provides the visual morphological
classifications of $\sim 1$ million galaxies from the Sloan Digital Sky Survey.
We find a non-zero mutual information between morphology and environment which
decreases with increasing length scales but persists throughout the entire
length scales probed. We estimate the conditional mutual information and the
interaction information between morphology and environment by conditioning the
environment on different length scales and find a synergic interaction between
them which operates upto at least a length scales of $ \sim 30 \, h^{-1}\, {\rm
Mpc}$. Our analysis indicates that these interactions largely arise due to the
mutual information shared between the environments on different length scales.
