  We will discuss theoretical and experimental results concerning comparison of
entropy of pseudo-Anosov maps and volume of their mapping tori. Recent study of
Weil-Petersson geometry of the Teichm\"uller space tells us that they admit
linear inequalities for both sides under some bounded geometry condition. We
construct a family of pseudo-Anosov maps which violates one side of
inequalities under unbounded geometry setting, present an explicit bounding
constant for a punctured torus, and provide several observations based on
experiments.
