Action At a Distance and the Second Law

[studiot]

Whilst musing on a statistical question I had a thought.

Consider an isolated box of gas.

The expectation is that the particles will be evenly distributed throughout the box.
This is shown in fig 1 where there are 3 particles in each subdivision.

Now as the particles move about consider the situation where two particles have temporarily moved from other divisions, B and D into division A.
This is shown in fig2

This constitutes a local decrease in entropy in A and an corresponding increase in B and D since the overall or global entropy must remain constant.

Now this must be true however small the divisions or however large the box.

So the question arises "How fast does the local balancing of total entropy spread throughout the box?" and ""Is this some sort of action at a distance in a big enough box?"

Edited September 3, 2020 by studiot

[MigL]

It is still information and constrained to move at less than/equal to c .
And, as a statistical process, a causal 'connection' has to be maintained between different sections.

[studiot]

2 hours ago, MigL said:

It is still information and constrained to move at less than/equal to c .
And, as a statistical process, a causal 'connection' has to be maintained between different sections.

Thank you for the reply MigL.

I don't find your statement convincing, however.

Surely the instant that a particle crosses a dashed line there must be a local entropy change, which must include the whole compartment.

I am exploring the compatibility of 'Laws' from different parts of Physics here and in particular testing the boundaries of classical thermodynamics.

It will be interesting to here what other members have to say.

[MigL]

But the local entropy must propagate while keeping a causal connection.
How would far parts of the compartment 'know' what is happening locally.

Maybe I'm not understanding the problem ...

[joigus]

The concept of entropy I'm familiar with is itself an average on the particle or state index (sum to all microscopic entities), and does not depend on time or space (sum or integral to all positions). 

I've sometimes heard the words "local entropy production" but I've always found them confusing.

It sounds to me like you're talking about fluctuations, but I don't see anything non-local in that either. Maybe I'm not understanding the problem either.

I'm also aware that you know much more about kinetics than I do.

[J.C.MacSwell]

On 9/3/2020 at 9:00 AM, studiot said:

 

This constitutes a local decrease in entropy in A and an corresponding increase in B and D since the overall or global entropy must remain constant.

Now this must be true however small the divisions or however large the box.

 

 

I don't think this is correct. First of all it can increase. Second, on the scale you are discussing it can decrease randomly.

[studiot]

1 hour ago, J.C.MacSwell said:

First of all it can increase

How for the entire isolated system?

1 hour ago, J.C.MacSwell said:

it can decrease randomly.

Again how for the entire system ?

[swansont]

What is the entropy for the system? And in the divisions?

[J.C.MacSwell]

On 9/4/2020 at 12:56 PM, studiot said:

How for the entire isolated system?

 

Increase? This is generally the most likely occurrence.

From Wiki:

"The second law of thermodynamics states that the entropy of an isolated system never decreases over time. Isolated systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy."  https://en.wikipedia.org/wiki/Entropy

On 9/4/2020 at 12:56 PM, studiot said:

Again how for the entire system ?

Decrease randomly?

The above would seem to contradict my claim that decreases can randomly occur, but in an isolated system at maximum entropy random fluctuations will still occur. This would allow a temporary decrease in entropy. 

This can actually happen in any isolated system (just don't count on it...the second law is on a very strong footing) though statistically less and less likely for any system further from maximum entropy and for more complex systems.

The system described is so simple that random increases and decreases in entropy is bound to occur at points over time. The second law notwithstanding.

Edited September 7, 2020 by J.C.MacSwell

[studiot]

On 9/4/2020 at 5:02 PM, swansont said:

What is the entropy for the system? And in the divisions?

Sorry I hadn't noticed this before.

1 hour ago, J.C.MacSwell said:

Increase? This is generally the most likely occurrence.

From Wiki:

"The second law of thermodynamics states that the entropy of an isolated system never decreases over time. Isolated systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy."  https://en.wikipedia.org/wiki/Entropy

Decrease randomly?

The above would seem to contradict my claim that decreases can randomly occur, but in an isolated system at maximum entropy random fluctuations will still occur. This would allow a temporary decrease in entropy. 

This can actually happen in any isolated system (just don't count on it...the second law is on a very strong footing) though statistically less and less likely for any system further from maximum entropy and for more complex systems.

The system described is so simple that random increases and decreases in entropy is bound to occur at points over time. The second law notwithstanding.

 

 

Let us pretend you haven't contradicted yourself, and analyse the overall sytem and subsystems.

The system is isolated

The subsystems are open.

All have internal energy.

The particles have kinetic energy, which does not change unless they hit something.

The instant a particle crosses (say from D to A as in the example), and before it hits anything in A its KE cannot change.

So sub system A gains this KE and subsystem D looses it.

Since there is no change of KE, no work is done and the First law tells us that the change must therefore be purely due to a heat transfer. (Which is to be epected)

Whilst that must lead to a change in entropy of both A and D, how does that lead to a change of entropy of the overall system?