Does Gibbs make a difference if you don’t know the equilibrium energy?

Well, not much, actually. At equilibrium, there is no such thing as free energy. There is something for some energy. I know that, but I didn’t actually write about it. Here is what I wrote:

The energy E is what you get when you combine an infinite number of particles with a constant energy

which means that, while energy E varies for any given particle, it is constant over time.

Okay, now Gibbs’ theorem is a big deal.

Okay, then Gibbs’ theorem isn’t a big deal.

Gibbs’ theorem is a big deal because in reality, we don’t know the equilibrium energy. We can measure the energy (see: temperature) between any two particles. But we don’t know how the energy changes over time. And, if you look at the diagram above, you might ask what if you take away the particles by a force?

Well, that might not change the equation, but what if the force is so strong that you can’t see the energy difference in time?

The answer is “nothing,” because the equation is still the same. There isn’t any free energy. What you need to know is how to measure the energy difference in time and, therefore, how to calculate the free energy of the particle.

But Gibbs hasn’t written about this. What will you get if you apply a force to a closed system that looks like this:

There is nothing for the energy E for the system to have for free energy. The net energy is still equal to zero, right? So, just because you don’t have knowledge of the equilibrium energy doesn’t mean that Gibbs’ theorem is not true. A force can change the amount of free energy for any given particle. We don’t want to change the equation, so if we assume that a force of zero is the mean value for all forces, then we’ll just write the solution:

The free energy of a closed system can fluctuation

I know we all know about free energy. If you look at Gibbs’ theorem, there isn’t an infinite number of closed systems. But what if you only looked at the right system.

When you have a system of particles, when you have any number of particles, how do you measure the energy. You might think that the energy of a system equals the sum and difference of the energy of the particles in

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