Entangled systems and heat transfer via holographic screens

Question

Suppose I have two extended bodies that are entangled to each other. Are the thermal properties of the objects affected in some way by entanglement?

For example, Imagine that one of the entangled objects is at some finite temperature in the vacuum of space, does the entanglement affect in any way the power lost via radiation?

If the entangled objects are considered as entangled Black Bodies,

• Do each body radiate proportional to the surface area of each individual object $A_1$ and $A_2$, independent from the area of the other?

• Do both objects radiate as a single black body with total area equal to $A_1 + A_2$?
  
   

Maybe if heat does not carry any information, can it be transferred in both directions between holographic screens, or horizons? it would seem that heat should not violate causality constraints that affect information transfer.

Comments

Entanglement on which state or pair of states? what is the link to the temperature?

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You need to explain what you mean by entangled thermal states. The latter are not pure, so the standard definition doesn't apply. 

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The way I understood the question was the following: start with a Bell state with the particles far away from another (let's say a few galaxies apart). Now let one of the particles interact with a heat bath. What can we say about the second particle? In particular, can we say the second particle has thermalized as well? (I guess not: the density matrix describing the second particle is given by tracing out the original Bell state on the left, using a thermal distribution on the left. But what is a thermal distribution for one particle need not be thermal for the second particle (?)) Interesting question though...

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@RubenVerresen: What can it mean for a single particle to thermalize? If the first particle would turn turns into some fixed polarization, the other would turn into the corresponding polarization determined by the entanglement. Thus if the first particle turns into a randomized polarization (whatever this could mean for a single particle), the second, would, too. Hence the second particle would thermalize, too, if this notion can be given a sensible meaning at all.

Answer 1

Entanglement is about states. Objects can carry such states but their other properties / states are in fine independent from the entangled states.

Let's now consider heating and for example two entangled polarization states.

Does heating the object carrying the entangled state on one side, lets us get a kind of polarization measurement ? I don't find how...

If you assume no , then you can conclude that they are unrelated and heating one from the pair doesn't affect the other.

Else , if you assume yes, what would happen ? the other spin state will adjust its polarization in a statistical way consistent with QM but I don't see how we can say something on the heat on this side.

Black body radiation of both objects behaves as usual.

Answer 2

Entanglement between two systems just means that they are correlated with each other, it does not mean that they are in any kind of contact with each other.

For two entangled systems that are at different temperature (for example due to the fact that one of them gets coupled to a heat bath) to equilibrate, they have to be in thermal contact such that the temperature gradient between them can be reduced by an appropriate heat flux.

However, the "link of entanglement" does neither allow the transport of information nor heat or anything else between the two systems. So if the entanglement is the only "coupling" between the two systems, the second system would not equilibrate to its partner system which is coupled to a heat bath for example.

That nothing can be transported between two systems if entanglement is the only link between them is supported by the more recent view that the entanglement between the systems can be visualised as a (nontraversable!) Einstein-Rosen bridge between them via the recently discovered ER=EPR correspondance.