Youtube says the 2nd Law is Broken.

[sethoflagos]

This has been a common trope running round most of the pop-science channels on Youtube over the last year or so. I won't name names but I guess some of you know some of the channels in question. 

It starts with a box with N particles randomly dotted around inside it. The presenter then changes the cartoon to one where all the dots are shown on the left hand side of the box and states 'Statistical Mechanics says that all random configurations of particles are possible, therefore sometime eventually this low entropy configuration will occur, therefore the 2nd Law only applies sometimes'.

Leaving aside the macroscopic shift in centre of mass that shows dereliction of the 1st Law (an easy fix if they cared about it), they present this extraordinary claim without stating what quantities are preserved in the analysis, what if anything has happened to the momentum distribution in the half box scenario, or whether 'statistical mechanics says' the system will ever find its way back to its original thermal equilibrium.

Have I missed something somewhere, or is it all just clickbait BS? 

 

Edited July 2, 2020 by sethoflagos

[mathematic]

Second law is statistical..  It is  possible for something weird to happen, but the probability is astronomically small.

[sethoflagos]

In what way is the 2nd Law 'statistical'? Many notable researchers have used a statistical approach to probe the complexities of thermodynamic systems, but isn't that only because of the computational complexity? Are you claiming that the systems themselves are stochastic in a real sense? If so, then where does the random element creep in? 

[swansont]

It comes from statistical mechanics 

“Statistical mechanics postulates that, in equilibrium, each microstate that the system might be in is equally likely to occur, and when this assumption is made, it leads directly to the conclusion that the second law must hold in a statistical sense. That is, the second law will hold on average, with a statistical variation on the order of 1/√N where N is the number of particles in the system. For everyday (macroscopic) situations, the probability that the second law will be violated is practically zero. However, for systems with a small number of particles, thermodynamic parameters, including the entropy, may show significant statistical deviations from that predicted by the second law. Classical thermodynamic theory does not deal with these statistical variations.”

https://en.wikipedia.org/wiki/Second_law_of_thermodynamics#Statistical_mechanics

[sethoflagos]

Many thanks, swansont.

My reading of this passage draws two key inferences:

1) 'Each microstate that the system maybe in' refers specifically and only to the ensemble of microstates whose properties are consistent with those of the initial microstate and for which there is a credible mechanism through which each can be accessed (see ergodic hypothesis). It most definitely does not include any wacky extreme non-equilibrium microstate dreamt up by a Youtube presenter in search of more Patreon support. 

2) A snapshot of a small number (like 42) particles doesn't have a precisely defined temperature etc due to the uncertainty principle and the relatively large error bars of a small dataset. However, this measurement problem is just that, isn't it? Hiding away inside the quantum fuzziness is there a possible state of 42 regularly spaced particles all with zero relative motion? I think not. There's no route in and out of such a state. I don't really follow quantum theory but I was under the impression that many of its leading lights were currently touting 'information cannot be destroyed' which pretty much underpins the 2nd Law, doesn't it?

Actually there's a third now I think of it. The Wikipedia paragraph you referenced carries no inline references. I was rather hoping to find something on this subject that's been through a proper peer review. 

 

  

 

[studiot]

A couple of things to add to swansont''s excellent post.

Firstly Thermodynamics largely ignore the time variable.

In particular it says nothing about how long a system will remain in a given state or how long it will take to reach that or another state.

So these so called second law violations are 'instantaneous' and short lived, but the second law always wins on a time averaged basis.

Secondly what makes you think these are actually formal 'states' ?

Formal states have state variables that are properly defined.

You cannot apply most of classical thermodynamics to improperly defined states.

 

[sethoflagos]

1 hour ago, studiot said:

A couple of things to add to swansont''s excellent post.

Firstly Thermodynamics largely ignore the time variable.

In particular it says nothing about how long a system will remain in a given state or how long it will take to reach that or another state.

So these so called second law violations are 'instantaneous' and short lived, but the second law always wins on a time averaged basis.

Secondly what makes you think these are actually formal 'states' ?

Formal states have state variables that are properly defined.

You cannot apply most of classical thermodynamics to improperly defined states.

 

Perhaps you didn't read my OP carefully - I dispute that these 'so-called second law violations'  exist at all precisely because they ignore the concept of formal states. In particular these examples depict what I presume is a microcanonical ensemble (no heat bath is indicated) which in statistical mechanics (as I understand it at least) has a clearly defined equilibrium NVE state. ie the ensemble consists of all those possible accessible permutations of that number of particles (N) occupying a constant volume (V) within a vanishingly thin band of total energy (E). I trust that you agree that this corresponds to a formal state.

The next slide presents (presumably) the same N particles occupying only half the volume, claiming that this an inescapable result of statistical mechanics. Would you agree that this corresponds to an entirely different formal state (with undefined total energy to boot)?

Personally, I dispute that such a state could evolve for even the briefest of flickers because in that instant, it 'forgets' its earlier state - the information necessary for restoring it has been irretrievably lost due to the proposed macroscopic drop in entropy. The change would be permanent. This is significant. If we accept the smallest possibility of such an event, we accept higher frequency occurrence of less extreme random deviations and so on until we no longer have meaningful conservation laws - isolated systems would be continuously changing their properties in a continuous random walk with expected deviation propotional to the square root of time elapsed. 

I am amazed that so many seem to buy into this concept, without apparently the slightest shred of empirical evidence.

 

 

   

    

[swansont]

7 hours ago, sethoflagos said:

Many thanks, swansont.

My reading of this passage draws two key inferences:

1) 'Each microstate that the system maybe in' refers specifically and only to the ensemble of microstates whose properties are consistent with those of the initial microstate and for which there is a credible mechanism through which each can be accessed (see ergodic hypothesis). It most definitely does not include any wacky extreme non-equilibrium microstate dreamt up by a Youtube presenter in search of more Patreon support. 

Who said they were non-equilibrium?

Quote

2) A snapshot of a small number (like 42) particles doesn't have a precisely defined temperature etc due to the uncertainty principle and the relatively large error bars of a small dataset. However, this measurement problem is just that, isn't it? Hiding away inside the quantum fuzziness is there a possible state of 42 regularly spaced particles all with zero relative motion? I think not. There's no route in and out of such a state. I don't really follow quantum theory but I was under the impression that many of its leading lights were currently touting 'information cannot be destroyed' which pretty much underpins the 2nd Law, doesn't it?

You didn’t indicate N=42 before, and regularly-spaced is a new addition, as well as zero relative motion. Where did these come from?

You can’t go changing the parameters like that.

 

Quote

Actually there's a third now I think of it. The Wikipedia paragraph you referenced carries no inline references. I was rather hoping to find something on this subject that's been through a proper peer review. 

Wikipedia articles like this are more like a textbook, but there’s more in the link.

On 7/2/2020 at 6:21 PM, sethoflagos said:

 

It starts with a box with N particles randomly dotted around inside it. The presenter then changes the cartoon to one where all the dots are shown on the left hand side of the box and states 'Statistical Mechanics says that all random configurations of particles are possible, therefore sometime eventually this low entropy configuration will occur, therefore the 2nd Law only applies sometimes'.

Not sure why you are thinking the system is low entropy.

[sethoflagos]

50 minutes ago, swansont said:

Who said they were non-equilibrium?

I did. A box of volume V with all its contained particles sat in the left half is a non-equilibrium state, isn't it? As were each and everyone of the previous10^(big) intermediate microstates necessary to create this scenario.  

53 minutes ago, swansont said:

You didn’t indicate N=42 before, and regularly-spaced is a new addition, as well as zero relative motion. Where did these come from?

You can’t go changing the parameters like that.

You're Wikipedia link introduced 'N .... a small number of particles'. I thought it might be useful to firm up the order of magnitude where this concept may have some significance. Something a bit smaller than say N = Avogadro's number.

Similarly, you're link stated this small number of particles 'may show significant statistical deviations from that predicted by the second law' without quantifying it by example. So I provided an example.

I wasn't changing the parameters. I was merely plugging in representative numbers where they had been left unquantified, woolly, and uninformative.    

55 minutes ago, swansont said:

Not sure why you are thinking the system is low entropy.

Please read the quote this comment refers to: it paraphrased the Youtube presenters. For me, the relative temperatures of the two states were undefined therefore so were the relative entropies.  

[Endy0816]

@sethoflagos

You can read about an experiment showing this here:

Quote

Denis J. Evans and colleagues have discovered, not how to beat the house, but what happens in the realm between a single coin toss and a weekend in Las Vegas. To do so they measured water molecules' influence the motion of tiny latex beads held between lasers.

They found that over periods of time less than two seconds, variations in the random thermal motion of water molecules occasionally gave individual beads a kick. This increased the beads' kinetic energy by a small but significant amount, in apparent violation of the second law.

The gain is short-lived, and so could never amount to a source of free energy or perpetual motion. But it is big enough to confirm what physicists have long suspected.

https://www.nature.com/news/2002/020722/full/news020722-2.html

Second Law is true on average though, so you won't ever see a cup spontaneously unbreak or all the air move to one side of a room.

Edited July 4, 2020 by Endy0816

[MigL]

As with everything else you see on YouTube, be prepared to do some research on your own ( in good old fashioned books ), to separate the wheat from the chaff, AND the 'made-up'.

[Mordred]

Text books are about the next best thing to formal training. I never pay attention to anything YouTube unless I can quarantee the poster is a well accredited physicist in the field of his or her expertise.

( The field of physics is highly diverse. I can quarantee someone like Swansont far beats my skills in his specialty. While I have my own specialty (cosmology)).

 So research on a topic should never be blind faith. If you cannot find numerous support on a theory by different professional opinions then be wary.

Lol though I give credits to Studiot for applied engineering physics, Marcus for relativity and Janus for astrophysics.

The information in this thread does not meet any criteria to question the second law in thermodynamics in any cosmology related studies I am familiar with including QFT related applications.

6 hours ago, sethoflagos said:

Perhaps you didn't read my OP carefully - I dispute that these 'so-called second law violations'  exist at all 

You are absolutely correct to question the above. So +1 for that.

Edited July 4, 2020 by Mordred

[swansont]

9 hours ago, sethoflagos said:

I did. A box of volume V with all its contained particles sat in the left half is a non-equilibrium state, isn't it? As were each and everyone of the previous10^(big) intermediate microstates necessary to create this scenario.  

What does equilibrium mean in terms of a gas?

 

Quote

You're Wikipedia link introduced 'N .... a small number of particles'. I thought it might be useful to firm up the order of magnitude where this concept may have some significance. Something a bit smaller than say N = Avogadro's number.

 

Quote

Similarly, you're link stated this small number of particles 'may show significant statistical deviations from that predicted by the second law' without quantifying it by example. So I provided an example.

 So the parameters are not well-defined in that situation - they can show large deviations. Also note I responded to your question about the 2nd law being statistical, not the OP.

The “small number” as applied to the OP is fabricated 

 

Quote

I wasn't changing the parameters. I was merely plugging in representative numbers where they had been left unquantified, woolly, and uninformative.    

You did, though. Your gas became regularly-spaced, with no relative motion. It’s true there’s no path to get to that state, but AFAIK, nobody is claiming that state exists

 

Quote

Please read the quote this comment refers to: it paraphrased the Youtube presenters. For me, the relative temperatures of the two states were undefined therefore so were the relative entropies.  

They are not “representative” if the videos you are decrying do not use them.

You are trying to use a response to one very specific question and apply it to a broader question, which does not necessarily share the same assumptions. Do you want to discuss the issue you brought up in the OP, fine - do that. You want to discuss issues arising in stat mech, fine - open a new thread and do that. Don’t mix them.

 

[sethoflagos]

You do like to nit-pick!

5 hours ago, swansont said:

What does equilibrium mean in terms of a gas?

Depends a little on context. Formally, in my day job, it usually infers that the system is in a state of minimum Gibbs Free Energy - e.g there are no bulk convective processes going on within it. 

For a constant V, T system (I rarely encounter these) it would be a state of minimum Helmholtz Free Energy. In the OP scenario, the presenters start with an equilibrium V, T condition and claim that it can evolve spontaneously to occupy only V/2.  This requires a bulk convective flow (eg a piston compressing it) and represents a fundamental change of state.

5 hours ago, swansont said:

You did, though. Your gas became regularly-spaced, with no relative motion. It’s true there’s no path to get to that state, but AFAIK, nobody is claiming that state exists

They are not “representative” if the videos you are decrying do not use them.

The presenters concentrate on the position distribution of their system and fail to mention any impact on the momentum distribution. Do we infer the temperature has remained constant (breaking the 1st Law and the 2nd)? Has it increased as it would if it had been compressed by a piston (2nd Law preserved but not the 1st)? Or indeed has it decreased. We are left to guess. The only clue we have is that the presenters claim to have 'proven' evolution to a low entropy condition. If we believe them, this eliminates the higher temperature case from consideration.  

What we are left with is a proposed sudden and significant random change of state breaking both 1st and 2nd Laws. It's perhaps a personal flaw, but I've a habit of ridiculing such proposals by highlighting an extreme case that becomes allowable if their assumptions are correct. Such as a spontaneous jump to absolute zero. Of course the presenters do not state this inference explicitly as it would make them appear very foolish. But I'm quite happy to point out a logical extension of their false reasoning.

 

 

 

[studiot]

19 hours ago, sethoflagos said:

Perhaps you didn't read my OP carefully - I dispute that these 'so-called second law violations'  exist at all precisely because they ignore the concept of formal states. In particular these examples depict what I presume is a microcanonical ensemble (no heat bath is indicated) which in statistical mechanics (as I understand it at least) has a clearly defined equilibrium NVE state. ie the ensemble consists of all those possible accessible permutations of that number of particles (N) occupying a constant volume (V) within a vanishingly thin band of total energy (E). I trust that you agree that this corresponds to a formal state.

I did read it, perhaps not carefully enough.
But I note that this thread has jumped around a good deal and plenty of additional material has been introduced but not in any coherent way.
I would also observe that I only added a couple of very small points to swanson'ts original response, although I consider my point important.

You do not seem to have addressed either of them.

I now find myself in the situation of being puzzled as to whether to proceed with classical macroscopic thermodynamics where the typical version of the second law is being misrepresented by your references. System Entropy can and does decrease in appropriate circumstances.

Or whether to look at the misapplication of statistics of your youtube reference. Misapplication is one word bullshit or baloney are others for those authors.

Edited July 4, 2020 by studiot

[swansont]

1 hour ago, sethoflagos said:

You do like to nit-pick!

Depends a little on context. Formally, in my day job, it usually infers that the system is in a state of minimum Gibbs Free Energy - e.g there are no bulk convective processes going on within it. 

For a constant V, T system (I rarely encounter these) it would be a state of minimum Helmholtz Free Energy. In the OP scenario, the presenters start with an equilibrium V, T condition and claim that it can evolve spontaneously to occupy only V/2.  This requires a bulk convective flow (eg a piston compressing it) and represents a fundamental change of state.

A piston means V isn’t constant.

 

1 hour ago, sethoflagos said:

The presenters concentrate on the position distribution of their system and fail to mention any impact on the momentum distribution.

position ≠ momentum 

 

1 hour ago, sethoflagos said:

Do we infer the temperature has remained constant (breaking the 1st Law and the 2nd)?

Why does it break these laws?

 

1 hour ago, sethoflagos said:

Has it increased as it would if it had been compressed by a piston (2nd Law preserved but not the 1st)? Or indeed has it decreased. We are left to guess. The only clue we have is that the presenters claim to have 'proven' evolution to a low entropy condition. If we believe them, this eliminates the higher temperature case from consideration.  

It’s not a low entropy condition, as such. Did they say that, or is that your interpretation?

 

1 hour ago, sethoflagos said:

What we are left with is a proposed sudden and significant random change of state breaking both 1st and 2nd Laws.

Saying that doesn’t make it true.

1 hour ago, sethoflagos said:

It's perhaps a personal flaw, but I've a habit of ridiculing such proposals by highlighting an extreme case that becomes allowable if their assumptions are correct. Such as a spontaneous jump to absolute zero. Of course the presenters do not state this inference explicitly as it would make them appear very foolish. But I'm quite happy to point out a logical extension of their false reasoning.

How does this allow a jump to absolute zero?

[sethoflagos]

1 hour ago, studiot said:

I did read it, perhaps not carefully enough.
But I note that this thread has jumped around a good deal and plenty of additional material has been introduced but not in any coherent way.
I would also observe that I only added a couple of very small points to swanson'ts original response, although I consider my point important.

You do not seem to have addressed either of them..

Your point that classical thermodynamics largely time independent, I accepted without seeing the need for further comment. Which was the other point?

1 hour ago, studiot said:

I now find myself in the situation of being puzzled as to whether to proceed with classical macroscopic thermodynamics where the typical version of the second law is being misrepresented by your references. System Entropy can and does decrease in appropriate circumstances.

I'm 100% with Mordred on this issue. Would you be happy to simplify the thread and leave it at that? 

1 hour ago, studiot said:

Or whether to look at the misapplication of statistics of your youtube reference. Misapplication is one word bullshit or baloney are others for those authors.

Then we are in agreement.

38 minutes ago, swansont said:

A piston means V isn’t constant.

Obviously.

Hope all is clear

Edited July 4, 2020 by sethoflagos
keyslip

[swansont]

 

34 minutes ago, sethoflagos said:

Hope all is clear

The piston was your introduction - which violates the conditions of the problem - so this clarifies nothing. 

[sethoflagos]

56 minutes ago, swansont said:

A piston means V isn’t constant.

My point. We're agreed.

58 minutes ago, swansont said:

position ≠ momentum 

Agreed.

59 minutes ago, swansont said:

Why does it break these laws?

The V/2 state perforce requires some combination of W and Q which must be reflected in a balancing change in U. 2nd Law implies a minimum increase in U (and hence T) under simple compression.

1 hour ago, swansont said:

It’s not a low entropy condition, as such. Did they say that, or is that your interpretation?

 They said it. 

1 hour ago, swansont said:

Saying that doesn’t make it true.

Obviously.

1 hour ago, swansont said:

How does this allow a jump to absolute zero?

Absolute zero microstates are allowed into their ensemble by their reasoning.  

14 minutes ago, swansont said:

 

The piston was your introduction - which violates the conditions of the problem - so this clarifies nothing. 

How do you propose to explain all the particles appearing in one half of the box? My inference is that there must be something equivalent to an undeclared piston compressing the system which, as you say, violates the conditions of the problem. That in itself is a clarification: the hypothesis is probably BS.

[studiot]

1 hour ago, sethoflagos said:

Your point that classical thermodynamics largely time independent, I accepted without seeing the need for further comment. Which was the other point?

I labelled my points firstly and secondly to help those who perhaps do not read postings carefully enough.

What is the difference between accepting firstly in your own mind but saying nothing about It and ignoring it?

Firstly is the key to the fluctuations you seem so keen to discuss.

 

Secondly is about the status of these fluctuations.

 

One thing that would be useful would be to state the version of the Second Law  we are meant to be comparing the situations described to  ?

 

31 minutes ago, sethoflagos said:

How do you propose to explain all the particles appearing in one half of the box? My inference is that there must be something equivalent to an undeclared piston compressing the system which, as you say, violates the conditions of the problem. That in itself is a clarification: the hypothesis is probably BS.

 

The issue is not to explain it but to ask how does it compare with the Second Law ?

 

Consider this

We rely on the observation that throughout the Universe electrons will be in the appropriate place and energy level for bonding and other activity (when required) despite the probability that they will be somewhere else at the appropriate time interval.

When you compare the number of instances of such activity we have observed, to the probability of them doing something else must be incredibly small.

Isn't the kinetic theory of gas molecules a coarser example of the same statistics?

Edited July 4, 2020 by studiot

[swansont]

1 hour ago, sethoflagos said:

My point. We're agreed.

Agreed.

The V/2 state perforce requires some combination of W and Q which must be reflected in a balancing change in U. 2nd Law implies a minimum increase in U (and hence T) under simple compression.

V doesn’t change.

 

1 hour ago, sethoflagos said:

Absolute zero microstates are allowed into their ensemble by their reasoning.  

No, that does not follow

 

1 hour ago, sethoflagos said:

How do you propose to explain all the particles appearing in one half of the box? My inference is that there must be something equivalent to an undeclared piston compressing the system which, as you say, violates the conditions of the problem. That in itself is a clarification: the hypothesis is probably BS.

Start with one ball, with some energy E, under the conditions of an ideal gas, in some box with rigid walls. Obviously, it can be anywhere in the box. Same thing for two. Wile they will occasionally collide and exchange energy and momentum, there is no mechanism that requires one ball be on each side. Two balls being on one side does not require a change in volume.

Three balls, four balls - still no mechanism. Any conclusion about their average position is statistical. It’s like a coin toss of multiple coins - it becomes less likely to get all heads, or all tails, but nothing prevents it. Now increase it to an arbitrary number N.

At what point does a mechanism manifest that prevents all the balls being on one side? What is that mechanism?

[sethoflagos]

5 minutes ago, swansont said:

Start with one ball, with some energy E, under the conditions of an ideal gas, in some box with rigid walls. Obviously, it can be anywhere in the box. Same thing for two. Wile they will occasionally collide and exchange energy and momentum, there is no mechanism that requires one ball be on each side. Two balls being on one side does not require a change in volume.

Three balls, four balls - still no mechanism. Any conclusion about their average position is statistical. It’s like a coin toss of multiple coins - it becomes less likely to get all heads, or all tails, but nothing prevents it. Now increase it to an arbitrary number N.

At what point does a mechanism manifest that prevents all the balls being on one side? What is that mechanism?

An interesting rabbit hole!

Firstly, consider what is happening to your system centre of mass, and account for its apparent irregular motion.

I look forward to your well considered response (which I'll not preempt here)

[Ghideon]

3 minutes ago, sethoflagos said:

Firstly, consider what is happening to your system centre of mass, and account for its apparent irregular motion.

I'll try not to interrupt your discussion, just a question: do you mean centre of mass of balls only, centre of mass of the balls + the box the balls bounce around in? Other?

[swansont]

10 minutes ago, sethoflagos said:

An interesting rabbit hole!

Firstly, consider what is happening to your system centre of mass, and account for its apparent irregular motion.

I look forward to your well considered response (which I'll not preempt here)

When the ball is traveling, the CoM is moving, so this isn’t necessarily a constraint but it’s an idealized system (we start with an ideal gas) so the container has a mass >> the mass of the gas. Effectively infinite mass. 

edit: xpost with Ghideon

[sethoflagos]

1 hour ago, studiot said:

Consider this

We rely on the observation that throughout the Universe electrons will be in the appropriate place and energy level for bonding and other activity (when required) despite the probability that they will be somewhere else at the appropriate time interval.

When you compare the number of instances of such activity we have observed, to the probability of them doing something else must be incredibly small.

Isn't the kinetic theory of gas molecules a coarser example of the same statistics?

Another interesting rabbit hole.

By coincidence, I asked a question the other day about the strength of coupling between a CMB photon emitter and its TV aerial absorber. Mordred informed me that contrary to what I'd inferred from what I'd read of GR, they weren't actually touching since the photon wasn't a valid frame of reference. Obviously, I've no grounds whatsoever for disputing this, and too many Minecraft projects planned to try and get to grips with it. I just accept that for now and the foreseeable future, such fields are beyond my understanding.

 

 

7 minutes ago, Ghideon said:

I'll try not to interrupt your discussion, just a question: do you mean centre of mass of balls only, centre of mass of the balls + the box the balls bounce around in? Other?

Not my system. You define your system as you wish. If you can. It's not easy, and perhaps will give some idea of why the microcanonical ensemble has given statistical mechanics some headaches in the past. The canonical and grand canonical ensembles find easier application in the real world and have no aberrant conflicts with classical thermodynamics.

11 minutes ago, swansont said:

When the ball is traveling, the CoM is moving, so this isn’t necessarily a constraint but it’s an idealized system (we start with an ideal gas) so the container has a mass >> the mass of the gas. Effectively infinite mass. 

edit: xpost with Ghideon

There is now an exchange of work between particles and box. 

It has become your very own 'undisclosed piston'. Do you now see and understand the issue?