From the manufacturer:
One thing has stayed consistent throughout John Petrucci’s long and successful career: the DiMarzio® pickups in his guitars. John has been pushing the envelope of progressive metal since the late eighties, and the DiMarzio® LiquiFire™ Neck Model resulted from our most recent collaboration with John. He used it throughout Dream Theater’s tenth studio album, "Black Clouds & Silver Linings". John swears this is the best live and studio sound he has ever had. He wanted a neck pickup with a flowing, singing solo tone when used with a heavily overdriven amp and a clear chord sound with a clean amp setting.
Since the mid 1990s, John’s neck pickup sound has been based on either the standard Air Norton™ or the custom version in his Ernie Ball® guitars. The LiquiFire™ has several significant differences. Its treble response is warmer and smoother while bass response is tighter and brighter. The total sound has a more focused voice which works equally well for highly overdriven solos and complex, clean chords.
Best videos/sound clips:
Here Guitar World's Paul Riario reviews the Crunch Lab bridge and LiquiFire neck pickups in a Reverend Les Paul-style guitar. The tones on display here are very much of the singing/crunchy Dream Theater variety, but some jazzy riffs come in at 2:27 with both pickups on.
Steve Kay here is playing some really expressive freestyle riffs through his Charvel San Dimas with the Crunch Lab bridge and LiquiFire neck. He switches back and forth between the pickups as the video goes on though you can see the selector in the video and he also has the pickup name appear on the screen so you know what you're listening to. Steve is playing through Amplitude with a Marshall Plexi modeled and a modeled tubescreamer driving it. Audio quality is only average but the playing makes this one a must-watch.
Dhalif here is playing some slow leads with delay on his Musicman Silhouette with Crunch Lab bridge and LiquiFire neck. Reminds me vaguely at times of Eric Johnson's Cliffs of Dover (note-wise not tone-wise). Played directly into a Line6 Pod X3. Very pretty.