Can Second Law of Thermodynamics / Entropy override Newton's Laws?

Can the Second Law of Thermodynamics / Entropy override Newton's Laws?

No. In the example given, every particle obeys Newton's laws. There is no particle that is not obeying $F=ma$.

From the example below, it seems that there is an underlying "Force" behind the second law of thermodynamics which drives it and which is more powerful than any other law and if there is a conflict between the second law of thermodynamics and any other law then second law will win. Is there really an underlying "force" behind the second law of thermodynamics, which drives the system in a particular direction?

Again, no. The second law describes how Newton's laws combine with the laws of probability. There is no other "force" acting in the problem.

Why is this demonstration not a violation of Newtonian mechanics? Well, consider this question: Does Newtonian mechanics say that heavy particles cannot move upwards?

What is happening in the beaker is that the many molecules are jostling around. The heavier molecules, on average, will be lower than the lighter molecules, since they will have the same amount of total energy, on average, but are heavier. But there are many, many molecules. Sometimes, the $NO_2$ molecules will have more kinetic energy, and bounce upwards.

The Second Law simply expresses that this random motion will result in a mixture of the gases. It does not contradict Newton's laws, but expresses the inevitable consequences of them.

The thermal motion has to be taken into account in any understanding of the example. It’s just as important as gravity.

  • if there was no gravity no gravitational force, zero gravitational potential) the gases would fully mix
  • if the temperature was zero (no thermal energy, no thermal motion) the gases would fully separate out.

When both effects are present, they have to balance out. And they do that through collisions and motions that obey both Newton’s laws and thermodynamics.

About the relation between Energy and Entropy:

About the demonstration of the denser gas diffusing to fill available space. I grant you that is counter-intuitive. We are accustomed to thinking that there is no such thing as spontaneously moving against a force. We expect that stones never roll uphill.

But yeah, in a sense that is what happens in the case of the denser than air gas diffusing in upwards direction; the denser gas is moving uphill.

So: energy isn't the only game in town, there's entropy too.

(No doubt there are also examples where energy and entropy are acting in the same direction, so that their influences add up. But it's interesting to see them pitted against each other.)

Whenever energy and entropy are acting in opposition to each other the system will evolve towards an equilibrium state.

You can manipulate where that equilibrium falls by manipulating the conditions. For instance, in biology labs a standard piece of equipment is a microcentrifuge.

Under normal gravity many components of cells remain in suspension. That is, under normal gravity the brownian motion effect is sufficient to keep everything in suspension. When a tube is spinning in the microcentrifuge everything in the tube is subject to a high G-load. The high G-load means that to move towards the bottom of the tube releases a lot more energy than under normal G-load. That shifts the equilibrium. With a sufficiently high G-load components settle out instead of remaining in suspension.

An extreme example of this is ultracentrifugation to separate isotopes of Uranium. This separation process is actually gas centrifugation. Uranium hexafluoride is gaseous. With the ultracentrifuge spinning sufficiently fast the level of separation of U-235 and U-238 can be pushed to a point where it is an economically viable way of enriching Uranium.

Note that centrifugation doesn't give complete separation. Furthest away from the spin axis the gas becomes somewhat U-238 enriched, the gas closer to the spin axis becomes somewhat U-238 depleted. Complete separation is too improbable to happen, even at the extreme spin rates of ultracentrifugation. The effect of the high G-load is that the equilibrium is shifted