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Maxwell's demon and comoving observers in general relativity: what do they have in common?
1  Instituto Universitario de Fisica Fundamental y Matematicas, Universidad de Salamanca, Salamanca, Spain


More than a century ago, J. C. Maxwell put forward a "paradox'', usually referred to as Maxwell's demon. The Maxwell's demon is a small "being'' living in a cylinder filled with a gas, and divided in two equal portions, by a partition with a small door. Then the demon may open the door when the molecules come from the right, while closing it when the molecules approach from the left. Doing so the demon is able to concentrate all the molecules on the left, reducing the entropy by NKln2 (where N is the number of molecules, and k is the Boltzman constant), thereby violating the second law of thermodynamics. It was necessary to wait for more than a century, until Bennet, gave a satisfactory resolution of this paradox.

Briefly speaking, Bennet pointed out that the irreversible act, which prevents the violation of the second law, is not the selection of molecules in order to put all of them in one side of the cylinder, but the restauration of the measuring apparatus (by means of which the selection is achieved), to the standard state, previous to the state where the demon knows from which side comes any molecule. The erasure of such information, according to the Landauer's principle, entails dissipation. In other words, to get the demon's mind back to its initial state, generates dissipation.

A somehow similar situation appears in general relativity.

Indeed, there is an ambiguity in the description of the source of the gravitational field. which is related to the arbritariness in the choice of the four--velocity in terms of which the energy--momentum tensor is split.

The above mentioned arbitrariness, in its turn, is related to the well known fact, that different congruences of observers would assign different four-velocities to a given fluid distribution. We have in mind here, the situation when one of the conguences corresponds to comoving observers, whereas the other is obtained by applying a Lorentz boost to the comoving observers.

The erasure of the information stored by comoving observers (vanishing three velocity), when going to the tilted observers, explains the presence of dissipative processes (included gravitational radiation) observed by the latter.

In this work we illustate this situation by analyzying an axially symmetric fluid which, for the commoving congruence of observers, are geodesic, shear-free, irrotational and non-dissipative, but now analyzed from the point of view of the tilted (Lorentz boosted) congruence. As expected from previous works, the fluid distribution appears to be dissipative for the tilted observer, as well as non-geodesic, nor shear-free and irrotational.

Furthermore, in this particular example, the tilted observer would detect a flux of gravitational radiation, associated to the magnetic part of the Weyl tensor, which for the tilted observers is non vanishing. The explanation for such a result is given in terms of the information theory, by analogy with the explanation by Bennet to resolve the Maxwell's demon paradox.

Keywords: Dissipative processes in general relativity; irreversibility; Landauer's principle; Maxwell's demos.