JPA 2.1 and Java EE 7 are such huge topics that it is impossible to give full credence to every item in the specification, however here are some miscellaneous features, which I think are well worth the pursuit. Let's start with custom JPQL functions.
Business applications that use a relational database have custom predefined SQL functions, which are beyond the JPA standard. In JPA 2.1, the query language has been extended to support invoking these custom functions, albeit your application is locked to a database vendor's server and schema.
SELECT a FROM Artist a, Lawyer m WHERE FUNCTION("ContractSignedOff", a.events, m.id )
Here is the JPQL example for the custom SQL function
ContractSignedOff, which is ...