Jim Day
Ansys Employee

Yes, E0 would be nonzero in *EOS_JWL when modeling a high explosive.   Values may be hard to come by owing to the sensitive nature of modeling HE.

A fairly common application of E0 in *EOS is to initialize atmospheric pressure in air using *EOS_LINEAR_POLYNOMIAL.   Look for the notes on air in the LS-DYNA Aerospace Working Group MGD (Modeling Guidelines Document).  Use Google to locate this document.