- #1

SteveMaryland

- 16

- 2

We start with "particles in a box". These particles (at t-zero) may exhibit a range of energies. We place this box of particles in a heat bath for a "long time" until we have thermal equilibrium - no net heat or mass transfer through the box.

Boltzmann says that in this equilibrium condition, a specific energy gradient (distribution) among the particles in the box will occur, and that this specific energy distribution will result in max system entropy per Lagrange.

Doesn't this violate the concept of spontaneous process? If hot and cold particles are placed in thermal contact, thermal energy will, spontaneously, diffuse until all energy gradient goes to zero. "Nature abhors a gradient".

But now Boltzmann says that an energy gradient will persist, even among a system of particles held under equilibrium conditions.

I understand that this distribution satisfies the Lagrange criteria for max entropy but it still does not make any sense. By extension, Boltzmann is saying that energy gradients will always persist, even in a universe that has reached max entropy.

It seems to me that the only way a system of particles can reach max entropy is when each of the particles has the SAME energy - all system energy becomes uniformly diffused among the particles, energy gradient decays to zero, and energy distribution curve decays to a singularity. How could it be otherwise?