All ordered structures could be
an inevitable consequence of quantum fluctuation.

In a previous article, it was proposed that the Kingdom of God might evolve from tiny particles. The evolution is a process from a simple system to a more ordered system. Where did the order come from? Does the second law of thermodynamics prevent the creation of order?

The second law of thermodynamics states that the entropy of a closed (isolated) system can never decrease. The entropy is a parameter for disorder. More order means less entropy. However, it must be noted that the second law applies to a "closed" system. Although the entropy of a closed system never decreases, the entropy of a local system within the closed system may decrease, as long as the total entropy of the closed system does not decrease. Therefore, ordered structures can be created in a local system. For instance, water molecules may combine to form more ordered liquid water. If the second law prevents the formation of ordered structures, we would never have rain.

Ilya Prigogine was the first to elucidate the creation of order from a non-equilibrium system. In 1977, he was awarded a Nobel Prize for his contribution in this area. According to his works, order can most likely be created in a closed system which is far from equilibrium. The reason is quite simple. When a closed system is in the equilibrium state, its entropy has reached a maximum value. The entropy of the closed system cannot increase further. Hence, there is no room to compensate for the entropy decrease of a local system within the closed system unless it is accompanied by an entropy increase in a neighboring local system. By contrast, if a closed system is far from equilibrium, its entropy will increase dramatically, which can compensate for a substantial entropy decrease of a local system. Thus, ordered structures are more likely to be created from a non-equilibrium state than an equilibrium state.

In a previous article, we assume that the bulk universe might begin with an empty space. Without Heisenberg's Uncertainty Principle, the bulk universe would remain empty forever. Fortunately, the Heisenberg's Uncertainty Principle allows quantum fluctuation to create certain particles from the vacuum. The particle's energy created by the quantum fluctuation is called the vacuum energy, which is the physical basis of the cosmological constant in Einstein's cosmological equations. In the presence of the vacuum energy, the bulk universe will never be in an equilibrium state, because the vacuum energy will produce a negative pressure (more info) which shifts the system further from an equilibrium state. Although the attractive gravitational force among particles tends to contract the space, the negative pressure has an anti-gravity effect to expand the space. More space will create more vacuum energy and the bulk universe may deviate further and further from the equilibrium state. The creation of the far-from-equilibrium state allows ordered structures to be formed.

Our braneworld is known to begin with the Big Bang, which contains an enormously high energy density and is extremely far from equilibrium. In order to reach an equilibrium state, our braneworld expanded rapidly, resulting in dramatic increase in entropy. This can compensate for the entropy decrease due to the formation of ordered structures such as galaxies, stars, planets and the life on Earth.

In contrast to the gigantic Big Bang, the Kingdom of God might begin with a whisper. Nothing spectacular had happened. No extremely large vacuum energy density was ever created, because quantum fluctuation can most likely create small vacuum energy density. As a result, the space expansion of the bulk universe should be a fairly slow process. The far-from-equilibrium state was gradually and naturally built up over a long period of time.

(Last updated: June, 2007)