The universe is dominated by a non-zero energy of the vacuum (ρ ) that is making the expansion of the universe accelerate. This acceleration produces a cosmic event horizon with an associated entropy ~ [1]. Thus, the smaller the value of , the larger the entropy of the event horizon. When 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: 10 122 k >> 10 1°3 k. Here we

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... the issue of how one might apply the maximum entropy production principle (MEPP) [2] to a cosmological scenario in which is treated as a variable. The growth of is a maximum when the energy density of the vacuum is a minimum, greater than zero. We derive an entropy-based probability for the values of and we find that low values of are most probable: P( )~ . This probability distribution is an MEPP-based constraint on that is independent of anthropic constraints and may help explain why the observed value of is ~2 orders of magnitude lower than expectations based on a combination of anthropic constraints and quantum physics [3] .