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.

The space-time is basically curved and dynamical. Thus our knowledge of universe must be extend to a dynamical curved space-time to understand the nature of the universe. The field theory in the curved space-time has shown that the evolution of space-time involving the field in the curved space-time leads to the particle creation. In other side, by employing thermodynamics to cosmology, we can learn about the source of current entropy content associated with the universe. From the quantum thermodynamics, one has been manifested that the inner friction stemming from the quantum fluctuations of field can produce the entropy. Using this approach, the particle creation due to the expansion of space-time beginning from the vacuum is shown as an entropic increase. considering an asymptotically flat Robertson-Walker space-time, the particle creation entropy is evaluated. Each special scale factor can be used to characterize the cosmic parameters. Thus, the dependence of particle creation entropy on the field parameters and the cosmic parameters allows us to recover information from the underling structure of the space-time. Also, by adding a difference function to this particle creation entropy, the well-known entanglement measure can obtained to investigate the entanglement of created particles.  The quantum fluctuations of vacuum stemming from dynamical space–time can be interpreted as the entanglement work. In fact, the entanglement entropy, measuring the mixedness of the primary state, is affected from the creation and the correlation of the particle.

During self-organization, internal entropy decreases and internal information content increases. Information parallels order increase and entropy decrease and is a reflection of the internal structure determining the efficiency of the processes. The principle of least action from physics states that every motion in nature happens with the least expenditure of the product of energy and time, which is the quantity of action. Therefore increasing action efficiency of those processes is obeying fundamental principles in science and leads to more advanced systems. We present results from our most recent simulations and data analysis of the positive and negative feedback loops between the characteristics of evolving complex systems. Those loops lead to exponential growth with sinusoidal oscillations which can be modeled with a system of coupled harmonic oscillators.  The solutions of this model provide an exponential equation superimposed with sinusoidal oscillations. The amplitude and frequency of those oscillations also grow exponentially with time.  This solution matches well data and gives us an insight in the feedback loops in evolving complex systems as a proposed mechanism for their observed exponential rates of self-organization and progressive development.