What documented comet has/had the highest specific orbital energy? After reading this answer I wondered if there have been document comets with orbits on non-return, hyperbolic trajectories as they approached the Sun.

This means that they would not be gravitationally bound to the sun, so either they came from outside the solar system, or they managed to gain energy through a collision, or close pass with a large planet like Jupiter.

The quickest way to find the comet with the "highest" orbit is to ask for the one with the largest specific orbital energy, the total energy (kinetic + potential) divided by the mass, (Joules/kg). For a bound orbit the value would be negative, for an unbound, non-returning orbit it would be positive.

Question: What documented comet has/had the highest specific orbital energy? It should be an identified object with a known or measured orbit, not just a generic, nameless "edge-of-the-Oort Cloud placeholder."
That is a very good timing for this question.

There is a comet with the name C/2017 U1 (PANSTARRS), that was just discovered a few days ago (on 18th October) which has an orbital eccentricity of 1.18, which is by far highest eccentricity recorded so far.

The eccentricity describes how strongly "elliptical" an orbit is and refers to the variable e in the formula of Kepler's orbit. 1.18 makes the orbit a hyperbolic one, meaning it is not an actual orbit, but has higher velocity than the required escape velocity and is basically just passing by in our solar system. And it's the first recorded comet so far that has an hyperbolic orbit.

This comet is the first candidate for an interstellar comet ever in recorded history. It is already pretty certain that it originated from interstellar space, but not official yet.

Quote from minorplanetscenter.net:


  Further observations of this object are very much desired.  Unless there
  are serious problems with much of the astrometry listed below, strongly
  hyperbolic orbits are the only viable solutions.  Although it is probably
  not too sensible to compute meaningful original and future barycentric orbits,
  given the very short arc of observations, the orbit below has e ~ 1.2 for
  both values.  If further observations confirm the unusual nature of this
  orbit, this object may be the first clear case of an interstellar comet.


Sources:


 http://www.minorplanetcenter.net/mpec/K17/K17UI1.html
 https://en.wikipedia.org/wiki/C/2017_U1_(PANSTARRS) 
 https://imgur.com/t/science_and_tech/vM4oh