Why Gibbs free energy is zero at equilibrium? – Bayesian Model Evidence


No one will ever know Gibbs’ initial energy at birth (as if that was not already known because we would have done an experiment a century ago by now), no one will ever know Gibbs’ net energy once it is in equilibrium with the rest of the universe (and thus no one is free to calculate the rate at which the entropy increases and decrease); and finally, the question of whether or not that initial energy remains at equilibrium is not a problem at all, because the only time Gibbs’ energy is in fact at zero there is no longer any possibility for all the particles and forces involved to exert any force on it. What remains is a small fluctuation in the energy of the system over time (like the fluctuations in the temperature of the earth over time), and it cannot be measured by any current instrument. It can only be found out by direct experiment. (No one would have made the effort at the beginning of the 19th century to find out just how little of the “equilibrium energy” in nature Gibbs had been able to discover!) The idea that we can measure Gibbs’ initial energy from this fluctuation in the system’s energy, without a microscope, is not a theory; it is plain wrong.

And the theory is wrong because it cannot account for the entropy. Gibbs’ initial energy is not zero at equilibrium, and in a universe in which the universe were infinite, it would be a constant. (If the universe were finite, the initial energy would be zero!) So we have two answers: either we have a theory of quantum mechanics, which is wrong and is not a theory of thermodynamics; or we have an analogy between the entropy and the motion of a particle that is an approximation. Neither of these two options have been proved in the real world, and we can prove them now because we have a quantum theory of quantum mechanics that makes the predictions we need in this particular situation. And the most important prediction in the real world—the predictions we need to see the world as a scientific observer would actually see the world as a scientist would see it:

“There is nothing wrong with thermodynamics, because its predictions are true, not just approximations, not hypotheses, but true predictions. The laws of thermodynamics are the laws of nature.” – Alan Guth

Theory 2: A quantum theory of quantum gravity

How do I get from theory 1: Gibbs’ initial energy at birth or theory 2: the entropy?

The answer is: You get there by assuming

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