Thermodynamic Basis of the Exclusion Principle

[Modey3]

Hello,

I was wondering if there has been any theoretical work regarding the thermodynamic justification of the Exclusion Principle. It is my view that all open systems proceed to the lowest free-energy state and all closed systems go to the highest entropy state. Of course, these states must be available.

modey3

 

[sokrates]

You have asked a very interesting question, but as far as I know there's no thermodynamic principle that predicts the exclusion principle. One problem of such a principle would be to be able to distinguish bosons in contrast to fermions because they don't have such an exclusion principle.

So as far as thermodynamics is concerned, you cannot justify exclusion principle bringing semi-classical arguments such as "marbles" and "spheres" to model particles as commonly done in thermo., say in deriving the Boltzmann distribution function.

So, others could correct me on this, but my take would be, no there isn't such easy justification, that would be wonderful if there WAS a reason though...

 

[alxm]

It sounds too 'soft' if you ask me.

AFAIK, the Pauli exclusion principle is absolute. There are no known violations of it. I'm pretty sure a violation of it would be fundamentally, mathematically at odds with QM. It's not prohibited for being too energetic, it's just not possible.

 

[sokrates]

He asked whether there was any thermodynamical basis for the exclusion principle, because at first sight it looks fundamentally in tension with "occupation of lowest energy state" arguments from thermodynamics.

Nobody was challenging the exclusion principle itself.

 

[alxm]

Then what's the problem? The states aren't available.

 

[D H]

He asked whether there was any thermodynamical basis for the exclusion principle, because at first sight it looks fundamentally in tension with "occupation of lowest energy state" arguments from thermodynamics.

The supposition arises from a misunderstanding of thermodynamics.

It is my view that all open systems proceed to the lowest free-energy state and all closed systems go to the highest entropy state.

Neither of those statements is true. There is no telling what an open system will do in general; it's open. Energy can come in or go out. A sufficiently small closed system can and has been observed to undergo violations of the second law of thermodynamics.

The laws of thermodynamics are statistical rather than absolute laws. A collection of a few hundred molecules or less can easily violate the second law of thermodynamics. Up that collection by a couple of orders of magnitude in number and violations becomes highly unlikely. For a collection of 10²³ molecules, the odds against a violation are effectively infinite. The exclusion principle is an absolute law. It is much deeper than the laws of thermodynamics.

 

[Modey3]

The supposition arises from a misunderstanding of thermodynamics.

Neither of those statements is true. There is no telling what an open system will do in general; it's open. Energy can come in or go out. A sufficiently small closed system can and has been observed to undergo violations of the second law of thermodynamics.

The laws of thermodynamics are statistical rather than absolute laws. A collection of a few hundred molecules or less can easily violate the second law of thermodynamics. Up that collection by a couple of orders of magnitude in number and violations becomes highly unlikely. For a collection of 10²³ molecules, the odds against a violation are effectively infinite. The exclusion principle is an absolute law. It is much deeper than the laws of thermodynamics.

Open systems can exchange energy/mass with its surroundings. If left unperturbed an open system will proceed towards the lowest energy state by exchange of energy with it surroundings. Closed systems cannot exchange energy with their surroundings, but are not precluded from internally generating entropy and hence proceed to a state where entropy is at a maximum. The entropy in this case cannot decrease as energy would need to be provided, but energy can't be provided since the system is closed.

I don't know what a sufficiently closed system is. In my experience there is no such thing as a truly closed system. It's more of a hypothetical assumption.

 

[xepma]

Open systems can exchange energy/mass with its surroundings. If left unperturbed an open system will proceed towards the lowest energy state by exchange of energy with it surroundings. Closed systems cannot exchange energy with their surroundings, but are not precluded from internally generating entropy and hence proceed to a state where entropy is at a maximum. The entropy in this case cannot decrease as energy would need to be provided, but energy can't be provided since the system is closed.

I don't know what a sufficiently closed system is. In my experience there is no such thing as a truly closed system. It's more of a hypothetical assumption.

That's a misconception again I'm afraid. Open systems are, by definition, in contact with some surrounding - for instance a small system in contact with a heat bath which has a temperature T. In that case the smaller system also tends to a (thermodynamic) state described by the temperature T. And that state is not the lowest energy state. Open systems rather tend to an equilibrium with their surrounding (temperature, chemical potential, etc).

 

[Modey3]

That's a misconception again I'm afraid. Open systems are, by definition, in contact with some surrounding - for instance a small system in contact with a heat bath which has a temperature T. In that case the smaller system also tends to a (thermodynamic) state described by the temperature T. And that state is not the lowest energy state. Open systems rather tend to an equilibrium with their surrounding (temperature, chemical potential, etc).

Yes of course an open system tends to equilibrium with it's surrounding. Suppose you define a temperature and chemical composition multi-dimensional energy surface which describes the particular closed system. THAT energy surface depends on the surroundings in which the open system is in contact with.