What is the definition of a system?What Constitutes a System?

[Saladsamurai]

Hello all! I am reading a thermodynamics text for a graduate course and I am running into some confusion early on. All throughout physics I thought that I knew what a system was; but, apparently I do not . Here is part of their definition and an example that I find confusing. It concerns the relationship between what is defined as a system and the external forces on that system.

<snip> ... Each external force on a given constituent of the system depends on the coordinates of that constituent and one or more external parameters that describe the overall effect of bodies in the environment, but not on the coordinates of a other constituent, either of the system or of bodies in the environment.

Here is their example that confuses me:

Two identical unrestrained magnets are near each other on a table but are unaffected by other magnets. Can we define one of the two magnets as a system?

Solution: No. The magnetic force depends explicitly on the coordinates of both magnets. Hence the two magnets are not separable. To proceed, we must include both magnets in the system

Any thoughts on this? I used to think that I could define a system in any manner that suits my needs for analysis; but, it now seems that is not the case. For anyone tha might have the text, I am reading from Thermodynamics: Foundations and Applications by Gyftopoulos and Baretta.

Edit

Maybe I should provide an example of what I believe is a system and someone can point out wherein lies the difference. An example that I feel is analogous to their 'magnet' example is the following. Suppose we have two blocks attached to one another by a string, one above the other (i.e. one block is dangling from the other via the string). There is a force built up in the string that imparts its effects to each block. I would say that I could isolate one block by making an imaginary 'cut' in the string to expose the force being exerted on each of the blocks. I could draw a free body diagram of the each block by simply drawing the block and the tensile force on each block as well as the weights of the blocks. Can I not now call each block a system?

 

[Saladsamurai]

Anyone want to talk about this one? It seems to be saying that we can define A to be a system if the external forces acting on A will not change if we move A to another location in space.

 

[my_wan]

Interesting. I generally assume I can arbitrarily define any subset as the system to, but the book has a point here. The question is, in the magnet example, if you wish to define them as separate system, how do you define the forces involved as separate for each magnet? It's not as simple as even a gas with a mixture of two different molecules as two systems. The forces on the magnets, even individually, are explicitly and inseparably dependent on both magnets. You can still refer to the position and momentum of each magnet as a separate system, but once you include the magnetic field, due to the vector cross product, there isn't a field definable by one or the other magnet alone.

 

[Saladsamurai]

Interesting. I generally assume I can arbitrarily define any subset as the system to, but the book has a point here. The question is, in the magnet example, if you wish to define them as separate system, how do you define the forces involved as separate for each magnet? It's not as simple as even a gas with a mixture of two different molecules as two systems. The forces on the magnets, even individually, are explicitly and inseparably dependent on both magnets. You can still refer to the position and momentum of each magnet as a separate system, but once you include the magnetic field, due to the vector cross product, there isn't a field definable by one or the other magnet alone.

I guess maybe my problem is that I never really knew what a system is. To me, "system" was always just a term that I assigned to the "thing" of interest. I never associated any stringent definition with it. It was just the thing that I drew the free body diagram of. And now that I am presented with this formal definition, I need to get used to it and pay a little more attention to what I call my system.

 

[brainstorm]

I always use the term system only because there are so many energy-transfers going on, that it would be difficult to talk about isolated interactions. E.g. a gas is a system because the momentum of any given molecule quickly disseminates throughout surrounding molecules to change the average energy of "the system." Am I looking at it wrong?

 

[dulrich]

You can still refer to the position and momentum of each magnet as a separate system, but once you include the magnetic field, due to the vector cross product, there isn't a field definable by one or the other magnet alone.

Is this true? I thought the whole point of the magnetic field was to separate the interaction of the two in a way that is definable for the one. In other words, the magnetic field captures the influence of all the other magnetic objects in the enviornment.

I'm with you on this one Saladsamurai. I can see someone arguing that you cannot separate a system that interacts in a way that is non-linear (and I'm not even sure about that).

I suspect that it is simply a semantics issue. Given their definition of system, it may follow that the individual magnets are not a system (I'm not sure). It might actually be good to see what is motivating the authors in this regard. Do they use this definition later in some derivation?

 

[my_wan]

I guess maybe my problem is that I never really knew what a system is. To me, "system" was always just a term that I assigned to the "thing" of interest. I never associated any stringent definition with it. It was just the thing that I drew the free body diagram of. And now that I am presented with this formal definition, I need to get used to it and pay a little more attention to what I call my system.

Yes, that is how I tend to think of a system, but not all systems are decomposable into parts without losing interesting aspects of the system.

Is this true? I thought the whole point of the magnetic field was to separate the interaction of the two in a way that is definable for the one. In other words, the magnetic field captures the influence of all the other magnetic objects in the enviornment.

The problem is that a magnetic field not only "captures" the influence of all the other magnetic objects in the environment, but also effects the properties of the magnetic field doing the the "capturing". In the case of an ideal gas consisting of two different kind of molecules, we can still consider it two systems. This is because we can uniquely identify the two types of molecules in all cases. But where two magnetic fields overlap, pick a point in that space, which magnetic field does that point in space belong to? Unlike the gas analogy, it doesn't have a unique identity to define a set ownership. Consider a single magnet, consisting of a large number of microscopic magnetic fields. Pick a point in space within the magnetic field and try asking which part of that magnet that point in the field belongs to. The question doesn't really make much sense. Two magnets with overlapping fields define a single field, and the topology of that field looks nothing like what both fields would look like linearly added together.

I suspect that it is simply a semantics issue. Given their definition of system, it may follow that the individual magnets are not a system (I'm not sure). It might actually be good to see what is motivating the authors in this regard. Do they use this definition later in some derivation?

In most cases what is or isn't a system is merely a semantics issue. In some case, like magnetic fields, there simply is no linear way to to divide the field components into separate parts in a way that always makes sense. If you are studying a system of ant behavior, it doesn't make much sense to ask which individual ant atoms a behavior belongs to. Emergent behaviors are ubiquitous in nature with or without life. If your system of interest involves emergent behaviors, even well defined ones, discussing that system at a level prior to the emergence of the system in question can be problematic. Although questioning the conditions leading to particular emergent behaviors can be interesting and informative.

 

[Andy Resnick]

Hello all! I am reading a thermodynamics text for a graduate course and I am running into some confusion early on. All throughout physics I thought that I knew what a system was; but, apparently I do not

It's not clear to me: by 'system', do you actually mean a *closed* system? Are you allowing or excluding open systems?

 

[brainstorm]

It's not clear to me: by 'system', do you actually mean a *closed* system? Are you allowing or excluding open systems?

Don't you answer your own question with your use of the term "open SYSTEMS?" If such a thing as an "open system" is thinkable, how could you exclude it's existence as a type of system?

 

[Saladsamurai]

It's not clear to me: by 'system', do you actually mean a *closed* system? Are you allowing or excluding open systems?

Hi Andy. I believe it supposed to be general. These folks take an unorthodox approach to everything, but I kind of like it. I have attached a pdf of the section on the definition of a system if anyone wants to look. Sorry about the scan quality, I did it with an iPhone app since my real scanner broke.

~Casey

EDIT: damn PDF file is too big to upload! It's 6.1 MB. The PF upload limit is 1.91 MB. Anyone know how I can get around this? Tried zipping it to no avail.

Double Edit: Just opened a free DropBox account Let's see if this works. You should be able to click http://dl.dropbox.com/u/8573618/SystemChapter.pdf" to download the PDF file.

 

[Andy Resnick]

Hi Andy. I believe it supposed to be general. These folks take an unorthodox approach to everything, but I kind of like it. I have attached a pdf of the section on the definition of a system if anyone wants to look. Sorry about the scan quality, I did it with an iPhone app since my real scanner broke.

~Casey

EDIT: damn PDF file is too big to upload! It's 6.1 MB. The PF upload limit is 1.91 MB. Anyone know how I can get around this? Tried zipping it to no avail.

Double Edit: Just opened a free DropBox account Let's see if this works. You should be able to click http://dl.dropbox.com/u/8573618/SystemChapter.pdf" to download the PDF file.

That pdf was an interesting read... is that Gyftopoulos and Baretta?

It seems they are dividing up the universe into "surroundings" and "system" in terms of restrictions on what can pass through the boundary. Their example of considering an O atom instead of a complete H2O molecule comes to mind.

But it seems a little sneaky- the environment can influence the system, but only under certain restrictions (which they discuss in terms of coordinates) which I don't quite understand. For example, the gravitational pull I am experiencing does depend on the coordinates of what I consider my environment (after all, I experience gravity due to the mass of Jupiter), so does that mean I am not separable from my environment?

And 'coordinates' can be more general than just position... they seem to be hung up on the idea of a system boundary, requiring it to be 'impermeable' in some sense. But Stokes' theorem allows the boundary to be arbitrary, without loss of generality.

As I said, it's an interesting read and I'd like to read more.

 

[Studiot]

Thank you for posing the question and introducing the reference, which I have not come across.

However just because one avowedly unconventional book offers a different definition of an established term there is no reason to abandon your term.

My Science and Technology Dictionary has "A System"

Generally anything formed of parts placed together or adjusted into a regular or connected whole

So we have
a system of forces
a system of rules
a system of gambling
a system of operation
etc

I think the important point are the words 'parts' and 'connected' (which I read as interacting in some way)

So we can distinguish a system from an individual object or entity.

Emergent? Well perhaps but not necessarily.

So is your single magnet a system?
I would say no it is a single entity.

Is your magnet plus the field around it a system ?
I would say yes because interaction can occur - one can affect the other.