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Can we describe the evolution of the cosmic event horizon with the maximum entropy production principle?
* 1 , 2 , * 1
1  Australian National University
2  University of Queensland


The universe is dominated by a non-zero energy of the vacuum (ρΛ) that is making the expansion of the universe accelerate. This acceleration produces a cosmic event horizon with associated entropy SCEH ~ ρΛ-1When this entropy is included in the entropy budget of the universe, it dominates the entropy of the next largest reservoir, supermassive black holes, by 19 orders of magnitude: 10122 k >> 10103 k. Here we address the issue of how one might apply the maximum entropy production principle (MEPP) to the processes responsible for the production of the cosmic event horizon entropy.

Keywords: maximum entropy production principle; expansion of the universe; cosmological constant
Comments on this paper
Ashwin Vaidya
What does "far from equilibrium" mean?
This is a very interesting result and I enjoyed reading your paper. In my own work on fluid solid interaction, I have found the MEPP to hold up when the system is sufficiently near thermodynamic equilibrium. However, our latest results (discussed in our paper A013) show that things are not as simple; when the nonlinearity of the system increases, governed by increasing Reynolds number, the system moves further away from equilibrium and the MEPP needs to be supplanted by the min-max of entropy production, defined in a very specific manner. This switch from near equilibrium-> "further away" or "far" from equilibrium happens at a very small Reynolds number which correlates with the onset of small scale turbulence.While we are continuing to compile more data to confirm our hypothesis, we believe that our system provides a possible way of clarifying the meaning of "far from equilibrium". In each of the examples where MEPP is being applied, it will be very helpful to identify more clearly what near equilibrium and far from equilibrium mean. Though this study is on a considerably more complex system than what we have been looking at, I wonder if it possible to make this distinction and if there are parameters (such as the Reynolds number in fluid mechanics) which determine the shift from "near" to "far"?

Charley Lineweaver
Hi Ashwin,
I will read your paper (A013) and get back to you. In cosmology there is something called bulk viscosity
which I think may be relevant, but I will need to read more about it to see if it could be used as to quantify "near" and "far". So far I have been content to use the variable Delta S = S_max - S_uni as a proxy for near and far....where S_max is the maximum entropy the universe will ever have ("heat death") and S_uni is the time dependent entropy of the universe.
Ashwin Vaidya
Hi Charley
Thanks for your reply and I look forward to continued conversation about this issue. It is fascinating that one can define a parameter like "viscosity" on a cosmological scale. Perhaps there is a "cosmological Reynolds number" which takes into account competing effects of inertia and bulk viscosity, as in a fluid?

It appears to me that the confusion and suspicion about the validity of the MEPP is at least partially due to the fact that we (those who employ it) have failed to articulate the precise context in which it is implemented. This is perhaps very difficult, but an important step in understanding the true merits of the MEPP. I'd also like to point out a new work which I found to be very interesting in this regard:

Hubler, A., Belkin, A. and Bezryadin, A. (2015), Noise induced phase transition between maximum entropy production structures and minimum entropy production structures?. Complexity, 20: 8–11.