A measure of disequilibrium in a system.

[geordief]

Does this exist?

If there is perfect equilibrium  then one example would be the heat death scenario and so  it's value must be zero.

But if temperature was the same throughout the system I think the value would also be zero .

If the temperature was not the same throughout the system how would one measure this globally ? (and can I call it a disequilibrium of the system ,with a value to represent the degree to which a disequilibrium was present?)

[studiot]

I think you first need to clarify your idea of equilibrium.

Equilibrium is essentially a two part concept.
A is in equilibrium with B

Very often this implies two opposing activities and the measure of equilibrium is the extent by which one is 'winning'.

If we normalise to percentages and create a scale then equilibrium occurs when A% = B% = 50%.

Then since at equilibrium, % disequilibrium must be zero

% disequilibrium = (% A - 50) %
Which can be positive or negative depending upon which way the activity is tending.

Note also we subdivide the equilibrium concept into many subcategories.

Mechanical Equilibrium (the origin of the concept)

Chemical Equilibrium

Thermal Equilibrium

Dynamic Equilibrium

Static Equilibrium

 

and so on

[geordief]

4 minutes ago, studiot said:

I think you first need to clarify your idea of equilibrium.

Equilibrium is essentially a two part concept.
A is in equilibrium with B

Very often this implies two opposing activities and the measure of equilibrium is the extent by which one is 'winning'.

If we normalise to percentages and create a scale then equilibrium occurs when A% = B% = 50%.

Then since at equilibrium, % disequilibrium must be zero

% disequilibrium = (% A - 50) %
Which can be positive or negative depending upon which way the activity is tending.

Note also we subdivide the equilibrium concept into many subcategories.

Mechanical Equilibrium (the origin of the concept)

Chemical Equilibrium

Thermal Equilibrium

Dynamic Equilibrium

Static Equilibrium

 

and so on

Well ,I was thinking along the lines of relative motion.

 

If the system is comprised of a finite number of elements then the relative motion of each element with any (and all)  other element can be summed globally  to produce a number. (and various sets of "sub numbers")

 

Can this/these  number/s be used to give a measure of the  disequilibrium  of the system as a whole?

 

Perhaps by comparing  successive measurements in time?

 

 

If we release a group of objects  ,in space say they will tend to move relative to each other and it may be possible to affect this relative motion by an energetic input  from a source that is outside the system ,introducing disequilibrium.

 

If this equilibrium could be measured ,would it be any kind of a function of the energy of that input (the direction  would presumably also be important)

[studiot]

 

9 minutes ago, geordief said:

Well ,I was thinking along the lines of relative motion.

 

If the system is comprised of a finite number of elements then the relative motion of each element with any (and all)  other element can be summed globally  to produce a number. (and various sets of "sub numbers")

 

Can this/these  number/s be used to give a measure of the  disequilibrium  of the system as a whole?

 

Perhaps by comparing  successive measurements in time?

 

 

If we release a group of objects  ,in space say they will tend to move relative to each other and it may be possible to affect this relative motion by an energetic input  from a source that is outside the system ,introducing disequilibrium.

 

If this equilibrium could be measured ,would it be any kind of a function of the energy of that input (the direction  would presumably also be important)

 

So what is A and what is B in all this ?

 

Remember equilibrium comes from the base root 'equal'

As does equation.

An equation has only two ' sides' - hence my A and B.

A = B  = C is really two equations.

[swansont]

If, for your system, equilibrium is signified by some variable that is minimized or maximized at equilibrium, you can measure how far away you are by measuring that variable (e.g. Gibbs free energy in certain thermodynamic systems). As studiot has noted, there are a number of different equilibria, so there's not likely to be one equation that applies to all systems.

 

[geordief]

A is the relative motion  between any two elements of the system and

B  is the same  relative motion  measured subsequently.

 

All these measurements can't be measured at the "same time" of course and so the delays  might have to be factored in  to create any global measurement.

 

 

 

Would that work?

 

22 minutes ago, studiot said:

 

 

So what is A and what is B in all this ?

 

Remember equilibrium comes from the base root 'equal'

As does equation.

An equation has only two ' sides' - hence my A and B.

A = B  = C is really two equations.

A is the relative motion  between any two elements of the system and

B  is the same  relative motion  measured subsequently.

All these measurements can't be measured at the "same time" of course and so the delays  might have to be factored in  to create any global measurement.

[swansont]

3 minutes ago, geordief said:

A is the relative motion  between any two elements of the system and

B  is the same  relative motion  measured subsequently.

All these measurements can't be measured at the "same time" of course and so the delays  might have to be factored in  to create any global measurement.

No relative motion means everything is at rest in the CoM frame. Thus the KE is minimized in that frame.

[geordief]

1 minute ago, swansont said:

In the CoM frame, this means everything is at rest. Thus the KE is minimized in that frame.

If the system is dynamic in an unbalanced way would that mean that a CoM could not be determined? 

 

Would such imbalances tend to disappear over time without external input?

[swansont]

Just now, geordief said:

If the system is dynamic in an unbalanced way would that mean that a CoM could not be determined? 

 

Would such imbalances tend to disappear over time without external input?

Not sure why the CoM could not be determined. What does "dynamic in an unbalanced way" mean?

 

[geordief]

1 minute ago, swansont said:

Not sure why the CoM could not be determined. What does "dynamic in an unbalanced way" mean?

 

Subject to external energetic input (from outside the system)

[swansont]

36 minutes ago, geordief said:

Subject to external energetic input (from outside the system)

Still don't see why you wouldn't be able to determine CoM. The system is accelerating, owing to the force you are exerting, which is the reason work is being done. But you should still be able to (in principle) determine the CoM, and the KE of the whole system

[studiot]

I repeat my suggestion that you try to narrow down your focus.

You seem to be mixing ideas from different subjects.

In particular you need to consider the question

What does relative velocity have to do with equilibrium?

[geordief]

8 minutes ago, studiot said:

I repeat my suggestion that you try to narrow down your focus.

You seem to be mixing ideas from different subjects.

In particular you need to consider the question

What does relative velocity have to do with equilibrium?

I have to go out  quite soon today . Perhaps it will give me a chance to mull it over  

[MigL]

As per your initial question, I'm not sure if global equilibrium is a sensible concept.

Globally only parts that are in causal contact can be in equilibrium.
And the parts of the universe that are in causal contact are continuously changing.
Parts that were in causal contact 1 bill yrs ago, are no longer.

You cannot say anything about the temp outside the observable universe.
 

[geordief]

On 12/10/2018 at 9:32 AM, studiot said:

I think you first need to clarify your idea of equilibrium.

Equilibrium is essentially a two part concept.
A is in equilibrium with B

Very often this implies two opposing activities and the measure of equilibrium is the extent by which one is 'winning'.

If we normalise to percentages and create a scale then equilibrium occurs when A% = B% = 50%.

Then since at equilibrium, % disequilibrium must be zero

% disequilibrium = (% A - 50) %
Which can be positive or negative depending upon which way the activity is tending.

Note also we subdivide the equilibrium concept into many subcategories.

Mechanical Equilibrium (the origin of the concept)

Chemical Equilibrium

Thermal Equilibrium

Dynamic Equilibrium

Static Equilibrium

 

and so on

I think (revisiting your first response to the OP) that  my implied idea of  two essentially homogeneous elements of a system  does not really fly.  but that , if it did  then  their state of equilibrium would (as per Swansont?)  have to be determined  relative to the CoM of the system as a whole (whether the CoM of the two elements was  in motion wrt the overall  system's CoM)

The system's CoM  would be changing all the time  unless the system was completely uniform.

Looking at my later replies  I think (embarrassingly) it is best to ignore them now ( as I  hadn't taken on board the importance of the CoM of the system as a whole (or any reference frame at all  to be honest)

I hope that I may  have a better idea of (dis) equilibrium  in terms of simple motion now. But if I have not  then I might have to withdraw from my own thread so as not to muddy the waters.

I have had a day to think about it now  and if this is still confused  then as I say it would be best if I butt out....

3 hours ago, MigL said:

As per your initial question, I'm not sure if global equilibrium is a sensible concept.

Globally only parts that are in causal contact can be in equilibrium.
And the parts of the universe that are in causal contact are continuously changing.
Parts that were in causal contact 1 bill yrs ago, are no longer.

You cannot say anything about the temp outside the observable universe.
 

Perhaps I used terms inappropriately. When I said "global" I was referring just to a finite system (not the existing universe)...  "global" in terms of the system as opposed to its pairs of sub-elements.

Would it now be possible/useful to describe such a system in terms of the state of equilibrium of these sub elements  to its CoM ?

[swansont]

23 minutes ago, geordief said:

 The system's CoM  would be changing all the time  unless the system was completely uniform.

A volume of gas in a balloon is not completely uniform, and yet its CoM is not constantly changing. Do you have an example of a system whose CoM would be changing all the time, in an unpredictable way? (if you can predict it, then you can account for it)

Newton's laws still apply. The body will be at rest or uniform motion unless there is a nonzero net force acting on it. That means the CoM will be fixed in the rest frame.

 

[geordief]

3 minutes ago, swansont said:

A volume of gas in a balloon is not completely uniform, and yet its CoM is not constantly changing. Do you have an example of a system whose CoM would be changing all the time, in an unpredictable way? (if you can predict it, then you can account for it)

Newton's laws still apply. The body will be at rest or uniform motion unless there is a nonzero net force acting on it. That means the CoM will be fixed in the rest frame.

 

What if the gas was composed of different elements with different properties such as perhaps density or charge?

[studiot]

43 minutes ago, geordief said:

I have had a day to think about it now  and if this is still confused  then as I say it would be best if I butt out....

No, don't give up yet.

 

The ideas behinbd this are so very important and fundamental, but they do not require advanced mathematics.

Just clear thinking.

I will only make one comment at this time.

 

What I think you are trying to do is to apply the concept of thermodynamic equilibrium to a mechanical situation.

One big difference between mechanical equilibrium and thermodynamic equilibrium is the thermodynamic idea of 'states' and state variables.
States and state variables have to apply to the system as a whole in thermodynamics, but not in mechanics.

MigL's comments really best apply to thermodynamics, where conservation laws can only be applied between the system and the rest of the universe, across a boundary. Swansont is concentrating on mechanical equilibrium where conservation laws can be applied between parts of the system.

Let me know if you want to pursue this.

 

Edited December 11, 2018 by studiot

[swansont]

2 hours ago, geordief said:

What if the gas was composed of different elements with different properties such as perhaps density or charge?

You mean like air? Air-filled balloons don't suffer from the problem you describe.

2 hours ago, studiot said:

 MigL's comments really best apply to thermodynamics, where conservation laws can only be applied between the system and the rest of the universe, across a boundary. Swansont is concentrating on mechanical equilibrium where conservation laws can be applied between parts of the system.

Only because that's what was described — defining equilibrium as having no relative velocities.

Thermodynamics has a pretty good handle on this. I already mentioned Gibbs free energy.