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We were discussing this article at work, particularly the quote:

“Finally, we can understand why a cup of coffee equilibrates in a room,” said Tony Short, a quantum physicist at Bristol. “Entanglement builds up between the state of the coffee cup and the state of the room.” The tendency of coffee — and everything else — to reach equilibrium is “very intuitive,” said Nicolas Brunner, a quantum physicist at the University of Geneva. “But when it comes to explaining why it happens, this is the first time it has been derived on firm grounds by considering a microscopic theory.”

And there was an inconsistency between our understandings that led to the question, "Can two independent particles become entangled, or can they only be entangled at the time of their creation?" The article certainly assumes the first. Is that the current understanding of entanglement?

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  • $\begingroup$ In an interacting theory two free particles can become "entangled": starting from a factorized state you will get, at finite times, a state that is no more factorized i.e. entangled. $\endgroup$
    – yuggib
    Commented Sep 24, 2014 at 14:48
  • $\begingroup$ So is the phrase "an interacting theory" descriptive of all schools of thought on quantum physics, or are there non-interacting variations? $\endgroup$
    – Don Branson
    Commented Sep 24, 2014 at 14:54
  • $\begingroup$ For interacting theory I mean a dynamics which is dictated by a self-adjoint Hamiltonian whose interaction part mixes between the particles. E.g. a potential $V(x_1,x_2)=V(x_1-x_2)$ where $x_1$ and $x_2$ are the coordinates of the two particles. $\endgroup$
    – yuggib
    Commented Sep 24, 2014 at 15:51

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Any two particles become entangled after an interaction. Entanglement is truly everywhere and occurs constantly.

The reaching of equilibrium of the temperature of a coffee cup and the room has not a lot to do with entanglement and more with the irreversibility of the motion of many particles (entropy).

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  • $\begingroup$ Note, though, that the irreversible motion of the particles does in general generate entanglement between the particles through their interactions. This is why people are researching entanglement, or quantum correlations, as a way to explain the arrow of time. However, the research is still in its infancy. $\endgroup$
    – Jasper
    Commented Sep 24, 2014 at 15:40
  • $\begingroup$ Occasionally I'll read of entangled particles being generated in a supercollider. So, is it correct then to understand that they're not generating new particles in an entangled state, but rather taking two particles and entangling them? $\endgroup$
    – Don Branson
    Commented Sep 24, 2014 at 19:22
  • $\begingroup$ I would require a bit more information to know the actual statement, but I think they mean the latter. Namely that after the collisions some particles are entangled with others, which definitely occurs. I would not see the point of generating specific entangled particles before you collide them. $\endgroup$
    – Jasper
    Commented Sep 25, 2014 at 10:37
  • $\begingroup$ Okay, that explains it. Thank you. The only point would be if particles wouldn't entangle later, but they do. The wording of those articles is ambiguous. $\endgroup$
    – Don Branson
    Commented Sep 25, 2014 at 13:51
  • $\begingroup$ Truthfulness of the claim depends on how do we understand “entanglement” and “interaction”. If we speak about state vectors (wave functions), and “interaction” is any Hamiltonian that isn’t $H_1\otimes I + I\otimes H_2$, then no, entanglement is not a necessary consequence of an interaction. See also my comment at physics.stackexchange.com/a/61756/56960 $\endgroup$
    – Incnis Mrsi
    Commented Oct 19, 2014 at 12:08

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