# Is the second law of thermodynamics routinely violated?
**URL:** https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151
**Category:** Factual Questions
**Created:** [April 28, 2019, 12:15am UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151 "2019-04-28T00:15:23Z")
**Posts on this page:** 20
**Page:** 8
### Author:  [@Max\_S](https://boards.straightdope.com/u/Max_S)
#### Post date: [May 8, 2019, 3:51pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/141 "2019-05-08T15:51:14Z")
> [@Half\_Man\_Half\_Wit](#):
>
> There is no change, merely an explanation. Entropy was introduced as a phenomenological quantity; a more accurate, more inclusive theory was found that explains what that quantity is.
>
> But this isn’t going to lead anywhere, is it. I’ve shown you quotes, arguments, and experiments, all of which explicitly disagree with you, and yet, to you, it still ‘seems like’ the second law should hold inviolable. You don’t give any reason for that, beyond your own belief.
>
> So let’s try something else. I’m going to try breaking things down as much as possible, so we can figure out where you actually don’t understand what I’m saying. Let’s start with a simple toy example.
>
> [ol]
> [li]Suppose you have a million coins.[/li][li]At every time-step t, a subset k of those coins are flipped.[/li][li]Which coins are flipped depends on which coins were flipped in the previous step, and how they landed.[/li][li]Coin-flipping is a perfectly deterministic process: given perfect knowledge of the initial state, the outcome would be exactly predictable.[/li][li]It is nevertheless meaningful to talk about a coin-flip coming up heads with 50% probability, since we never have that perfect knowledge.[/li][li]At any time-step, roughly half of the k coins are going to come up heads.[/li][li]Nevertheless, it is possible for all of them to come up tails.[/li][li]Suppose we start with all of the coins tails up.[/li][li]Each time-step is going to drive the system closer to 50% heads, 50% tails, on average. [/li][li]Suppose, for instance, that heads and tails are colored black and white, respectively, and you can only observe the aggregate color; then, the system is going to get closer to ‘grey’ over time.[/li][li]There is exactly one way to realize the initial state.[/li][li]There are many more ways to realize the state ‘50% heads, 50% tails’.[/li][li]Virtually all the time, we’re going to see a state that’s away from ‘50% heads, 50% tails’ evolve towards that state.[/li][li]Nevertheless, occasionally, at some time-step, all of the coins (or a sizable majority of them) are going to come up heads.[/li][li]Occasionally, if we wait long enough, we’re going to see the system evolve away from ‘50% heads, 50% tails’.[/li][li]These departures can take on an arbitrary length—two time-steps in which there is an evolution into the other direction may occur one after the other.[/li][li]Waiting long enough, we’re going to see the system get as far from ‘50% heads, 50% tails’ as we want.[/li][li]Suppose we had, after watching the system for some time, formulated a law: ‘the system will always become more grey over time’. [/li][li]Alternatively, we could say that the quantity G = 1 - (1 - 2K)^2, where K is the ratio of heads to tails, always tends to the maximum. This quantity assumes it maximum at K = 1/2, and is zero both for K = 0 (all white) and K = 1 (all black), and thus, captures what we mean by ‘the system will always be more grey over time’ at least in that respect.[/li][li]This law, even though we had thought it to be exact, in fact only holds on average. [/li][li]If we wait long enough, we will observe violations of this law. Sometimes, the system will become more white, or more black; equivalenty, sometimes, a time-step will lead to a decrease of G.[/li][/ol]
>
> If you disagree with any of the above, please tell me exactly with what, and why.
At step 5. you diverge from classical dynamics into statistical mechanics, and any pronouncement of laws thereafter (18) are not proper physical laws. You have disproved a law that I never defended. The laws of physics don’t care whether you know all the details or not, a law is still inviolable and a single actual violation disproves the law. The process that determines k is salient to any law, and applying the analogy to thermodynamics, there is no process k which can flip a coin from white to black without flipping exactly one other coin from black to white, and vice versa. Thus the average color of all coins never changes. That is the second law of thermodynamics applied to your hypothetical.
~Max
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### Author:  [@Kent\_Clark](https://boards.straightdope.com/u/Kent_Clark)
#### Post date: [May 8, 2019, 4:06pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/142 "2019-05-08T16:06:00Z")
IANAPhysicist, but it seems to me the Laws of Physics don’t have any legal standing. If any of them were “routinely” violated wouldn’t the physics community simply stop calling it a Law?
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### Author:  [@Chingon](https://boards.straightdope.com/u/Chingon)
#### Post date: [May 8, 2019, 6:00pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/143 "2019-05-08T18:00:16Z")
It’s historical verbiage.
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### Author:  [@DPRK](https://boards.straightdope.com/u/DPRK)
#### Post date: [May 8, 2019, 6:19pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/144 "2019-05-08T18:19:16Z")
> [@Max\_S](#):
>
> The paper in question is titled “Experimental Demonstration of Violations of the Second Law of Thermodynamics for
> Small Systems and Short Timescales” and **Half Man Half Wit** clearly [POST=21620578]cited[/POST] it as an experiment demonstrating violations of the second law. From the paper:
Please revisit the quote from Searles and Evans in Post #74, or simply observe that the (slightly misleading?) title refers to “small systems and short timescales” which is the precise opposite of the thermodynamic limit. But why lose sleep over the provocative title when the mathematical formulation is clear, and is related to a very general phenomenon?
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### Author:  [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)
#### Post date: [May 8, 2019, 6:52pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/145 "2019-05-08T18:52:55Z")
> [@Max\_S](#):
>
> At step 5. you diverge from classical dynamics into statistical mechanics, and any pronouncement of laws thereafter (18) are not proper physical laws.
This is both wrong and irrelevant. Irrelevant, because I wasn’t talking about classical dynamics, and hence, couldn’t well diverge from them—I was talking about coins. Wrong, because it’s completely well-defined to talk about probabilities in classical physics. A dice, once thrown, is completely describable classically. Yet, it’s meaningful to say that it comes up any given number 1/6th of the time. This you can take for a shortening of the following statement: ‘one sixth of all possible evolutions of the dice end with it showing any given number’. As you already accept that one can choose initial conditions randomly, it follows that with probability 1/6th, we have chosen an initial condition that’ll lead to it showing, say, a three, once it comes to rest.
Anyway, I presume that, if that was your only objection, you accept the conclusion—that, observing the system (talking just about the coins here), one might formulate a law to the effect that ‘greyness only increases’, and further, that this law can be violated?
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### Author:  [@Max\_S](https://boards.straightdope.com/u/Max_S)
#### Post date: [May 8, 2019, 6:55pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/146 "2019-05-08T18:55:28Z")
> [@DPRK](#):
>
> Please revisit the quote from Searles and Evans in Post #74, or simply observe that the (slightly misleading?) title refers to “small systems and short timescales” which is the precise opposite of the thermodynamic limit. But why lose sleep over the provocative title when the mathematical formulation is clear, and is related to a very general phenomenon?
I don’t think the underlying fluctuation theorem is clear at all, because it doesn’t make sense to me to compare statistical entropy of a system at two different times. The probability distribution of microstates at time t[SUB]1[/SUB] should be different than the equiprobability assumed at t[SUB]0[/SUB].
Neither do I think the second law of thermodynamics is statistical in nature, nor that it only applies for large systems. So long as a system has heat, temperature, and pressure, it should be a thermodynamic system subject to the laws of thermodynamics.
~Max
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### Author:  [@DPRK](https://boards.straightdope.com/u/DPRK)
#### Post date: [May 8, 2019, 7:52pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/147 "2019-05-08T19:52:56Z")
> [@Max\_S](#):
>
> I don’t think the underlying fluctuation theorem is clear at all, because it doesn’t make sense to me to compare statistical entropy of a system at two different times. The probability distribution of microstates at time t[SUB]1[/SUB] should be different than the equiprobability assumed at t[SUB]0[/SUB].
>
> Neither do I think the second law of thermodynamics is statistical in nature, nor that it only applies for large systems. So long as a system has heat, temperature, and pressure, it should be a thermodynamic system subject to the laws of thermodynamics.
>
> ~Max
OK, so you are wondering how entropy can be produced in a system that is not at equilibrium? The precise details depend on the dynamics of the (possibly many-body) system in question and potentially tricky to work out, but one can see what happens in various models, for instance there could be a stochastic noise term (like in Brownian motion), or your system can otherwise be modelled as a Markov process incorporating some randomness, or it may arise when your system satisfies chaotic/mixing/ergodic properties. These are good questions, and people have written books on the subject.
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### Author:  [@Max\_S](https://boards.straightdope.com/u/Max_S)
#### Post date: [May 8, 2019, 8:55pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/148 "2019-05-08T20:55:15Z")
> [@DPRK](#):
>
> OK, so you are wondering how entropy can be produced in a system that is not at equilibrium? The precise details depend on the dynamics of the (possibly many-body) system in question and potentially tricky to work out, but one can see what happens in various models, for instance there could be a stochastic noise term (like in Brownian motion), or your system can otherwise be modelled as a Markov process incorporating some randomness, or it may arise when your system satisfies chaotic/mixing/ergodic properties. These are good questions, and people have written books on the subject.
If statistical and classical entropy really are the same thing, classical non-equilibrium thermodynamics says dQ implies dS. There’s no reason to get into stochastic or chaotic microscopic models to make that point.
Actually I was wondering how entropy can increase (or decrease!) in an isolated system as **Half Man Half Wit** seems to imply it does.
~Max
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### Author:  [@Max\_S](https://boards.straightdope.com/u/Max_S)
#### Post date: [May 8, 2019, 9:02pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/149 "2019-05-08T21:02:55Z")
> [@Half\_Man\_Half\_Wit](#):
>
> This is both wrong and irrelevant. Irrelevant, because I wasn’t talking about classical dynamics, and hence, couldn’t well diverge from them—I was talking about coins. Wrong, because it’s completely well-defined to talk about probabilities in classical physics. A dice, once thrown, is completely describable classically. Yet, it’s meaningful to say that it comes up any given number 1/6th of the time. This you can take for a shortening of the following statement: ‘one sixth of all possible evolutions of the dice end with it showing any given number’. As you already accept that one can choose initial conditions randomly, it follows that with probability 1/6th, we have chosen an initial condition that’ll lead to it showing, say, a three, once it comes to rest.
>
> Anyway, I presume that, if that was your only objection, you accept the conclusion—that, observing the system (talking just about the coins here), one might formulate a law to the effect that ‘greyness only increases’, and further, that this law can be violated?
I meant to say your analogy of flipping coins ceased to apply to the current discussion at step 5.
I will concede that one might formulate a law to the effect that ‘greyness only increases’, and further, that law can be violated. What is your point?
~Max
---
### Author:  [@Max\_S](https://boards.straightdope.com/u/Max_S)
#### Post date: [May 8, 2019, 9:14pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/150 "2019-05-08T21:14:21Z")
> [@Half\_Man\_Half\_Wit](#):
>
> Wrong, because it’s completely well-defined to talk about probabilities in classical physics. A dice, once thrown, is completely describable classically. Yet, it’s meaningful to say that it comes up any given number 1/6th of the time. This you can take for a shortening of the following statement: ‘one sixth of all possible evolutions of the dice end with it showing any given number’. As you already accept that one can choose initial conditions randomly, it follows that with probability 1/6th, we have chosen an initial condition that’ll lead to it showing, say, a three, once it comes to rest.
It is meaningful to say the dice has a 1/6 probability of turning up any particular number. It is meaningful to say the dice will turn up any particular number after six trials. But neither of these statements follow from the premises. You never did fill in my syllogism:
[ul][li]Max’s die is a six-sided die.[/li][li]?[/li][li]Therefore, Max’s die is a die with a 1/6 probability of landing on any particular side.[/ul][/li]
I think the minor premise should read: “A six-sided die is a die with a 1/6 probability of landing on any particular side”.
Then we have another blank here:
[ul][li]Max’s die is a die with a 1/6 probability of landing on any particular side.[/li][li]?[/li][li]Therefore, Max’s die is a die that _will_ land on a particular side 1/6 of the time.[/ul][/li]
~Max
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### Author:  [@Max\_S](https://boards.straightdope.com/u/Max_S)
#### Post date: [May 8, 2019, 9:24pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/151 "2019-05-08T21:24:29Z")
> [@Half\_Man\_Half\_Wit](#):
>
> But this isn’t going to lead anywhere, is it. I’ve shown you quotes, arguments, and experiments, all of which explicitly disagree with you, and yet, to you, it still ‘seems like’ the second law should hold inviolable. You don’t give any reason for that, beyond your own belief.
I think I see where we misunderstand each other. I do not believe the second law is inviolable because it is the second law of thermodynamics. I think the second law is inviolable because I know of no examples of a violation, theoretical or observed.
You say it has been violated, but in each case I can’t see the violation without assuming some stochastic fundamental reality which also leaves the door open for violations of every other law of physics.
For example the random hopping in your first hypothetical means microscopic particles don’t obey physics at all. I never saw a violation to begin with for the billiard table or the laser experiment.
~Max
---
### Author:  [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)
#### Post date: [May 8, 2019, 9:39pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/152 "2019-05-08T21:39:34Z")
> [@Max\_S](#):
>
> I meant to say your analogy of flipping coins ceased to apply to the current discussion at step 5.
>
> I will concede that one might formulate a law to the effect that ‘greyness only increases’, and further, that law can be violated. What is your point?
>
> ~Max
Don’t worry about that for now. This is going to be a bit of a journey, and you keep running into confusions by getting ahead of yourself. But for now, the first step has been taken: we agree that it’s possible to have a law, valid to all appearances in the macroscopic realm, concerning a certain quantity (‘greyness’) such that once that quantity has been understood on a microscopic level, we understand that the original law can only hold in an approximate sense. We can build from here.
Now, to the next step.
[ol]
[li]Suppose you have two boxes, A and B.[/li][li]Box A is filled with white marbles, and box B is filled with black ones.[/li][li]Both boxes are placed on a vibrating plate, such that the marbles in them bounce around.[/li][li]The walls of the boxes are removable.[/li][li]Suppose you put both boxes next to one another, and remove the now adjacent walls, creating one big box.[/li][li]Marbles from the white box A will bounce into the black box, and marbles from the black box B will bounce into the white box.[/li][li]There are more ways of realizing a state that’s pretty uniformly grey, than there are to realize a state that’s (say) all white in box A, and all black in box B.[/li][li]Consequently, there are more ways to go from a state that’s slightly inhomogeneous to one that’s more homogeneous, than there are ways to go to a state that’s even more inhomogeneous.[/li][li]To any observer who, as before, is only capable of seeing gross colors, the formerly black-and-white separated box will gradually tend to a shade of even gray.[/li][li]That observer might formulate a law, stating that black and white, if brought into contact, eventually even out to a uniform gray.[/li][li]Knowing the microscopic description, we know that this is just, again, a law of averages: there is nothing that prohibits, say, all or a sizable fraction of the white marbles from bouncing back into box A.[/li][li]Given a long enough timescale, the even grey will, eventually, separate into black and white patches.[/li][/ol]
I expect greater resistance with this example. But again, try not to think ahead to the rest of this discussion; just consider the above system, as I have presented it. Do you agree that the conclusion is reasonable, here? That there is once again a law that appears valid thanks to the limited observations made at the macroscale, which we can see must be violated once we know about the microscopic level?
---
### Author:  [@DPRK](https://boards.straightdope.com/u/DPRK)
#### Post date: [May 8, 2019, 9:59pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/153 "2019-05-08T21:59:22Z")
> [@Max\_S](#):
>
> If statistical and classical entropy really are the same thing, classical non-equilibrium thermodynamics says dQ implies dS. There’s no reason to get into stochastic or chaotic microscopic models to make that point.
ok…? Not sure what you mean here (nor what is “classical non-equilibrium thermodynamics”); are you talking about Gibbs’s canonical ensemble?
> [@](#):
>
> Actually I was wondering how entropy can increase (or decrease!) in an isolated system as **Half Man Half Wit** seems to imply it does.
You start out in some improbable state, but then randomness and/or chaos mixes shit up.
---
### Author:  [@Max\_S](https://boards.straightdope.com/u/Max_S)
#### Post date: [May 8, 2019, 10:20pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/154 "2019-05-08T22:20:58Z")
> [@DPRK](#):
>
> ok…? Not sure what you mean here (nor what is “classical non-equilibrium thermodynamics”); are you talking about Gibbs’s canonical ensemble?
No, I just meant applying Clausius’s definition of entropy to a system with external net heat flow, that is, a system that is not isolated.
> [@DPRK](#):
>
> You start out in some improbable state, but then randomness and/or chaos mixes shit up.
But that’s just my point, assuming microscopic randomness or chaos means a particle can violate any number of laws. Not just the second law of thermodynamics.
~Max
---
### Author:  [@Max\_S](https://boards.straightdope.com/u/Max_S)
#### Post date: [May 8, 2019, 10:37pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/155 "2019-05-08T22:37:19Z")
> [@Half\_Man\_Half\_Wit](#):
>
> Don’t worry about that for now. This is going to be a bit of a journey, and you keep running into confusions by getting ahead of yourself.
Got it. I’ll go with you, one step at a time.
> [@Half\_Man\_Half\_Wit](#):
>
> But for now, the first step has been taken: we agree that it’s possible to have a law, valid to all appearances in the macroscopic realm, concerning a certain quantity (‘greyness’) such that once that quantity has been understood on a microscopic level, we understand that the original law can only hold in an approximate sense. We can build from here.
First I want to point out that the law from the coin example is not valid, was not formulated on a valid basis, and need not even appear to be valid. It is possible to observe greyness decreasing on a macroscopic scale in the previous example. The law was formulated nonetheless.
> [@Half\_Man\_Half\_Wit](#):
>
> Now, to the next step.
> [ol]
> [li]Suppose you have two boxes, A and B.[/li][li]Box A is filled with white marbles, and box B is filled with black ones.[/li][li]Both boxes are placed on a vibrating plate, such that the marbles in them bounce around.[/li][li]The walls of the boxes are removable.[/li][li]Suppose you put both boxes next to one another, and remove the now adjacent walls, creating one big box.[/li][li]Marbles from the white box A will bounce into the black box, and marbles from the black box B will bounce into the white box.[/li][li]There are more ways of realizing a state that’s pretty uniformly grey, than there are to realize a state that’s (say) all white in box A, and all black in box B.[/li][li]Consequently, there are more ways to go from a state that’s slightly inhomogeneous to one that’s more homogeneous, than there are ways to go to a state that’s even more inhomogeneous.[/li][li]To any observer who, as before, is only capable of seeing gross colors, the formerly black-and-white separated box will gradually tend to a shade of even gray.[/li][li]That observer might formulate a law, stating that black and white, if brought into contact, eventually even out to a uniform gray.[/li][li]Knowing the microscopic description, we know that this is just, again, a law of averages: there is nothing that prohibits, say, all or a sizable fraction of the white marbles from bouncing back into box A.[/li][li]Given a long enough timescale, the even grey will, eventually, separate into black and white patches.[/li][/ol]
>
> I expect greater resistance with this example. But again, try not to think ahead to the rest of this discussion; just consider the above system, as I have presented it. Do you agree that the conclusion is reasonable, here? That there is once again a law that appears valid thanks to the limited observations made at the macroscale, which we can see must be violated once we know about the microscopic level?
I take issue with step 9. I have no reason to believe the observer will observe a gradual change in color. You say the observer can only see gross color. If before he could distinguish two boxes of different colors, as soon as you remove the walls I take it he can only observe the combined box as a whole. Therefore the instant you remove the wall the observer sees flat grey.
~Max
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### Author:  [@Max\_S](https://boards.straightdope.com/u/Max_S)
#### Post date: [May 8, 2019, 10:43pm UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/156 "2019-05-08T22:43:33Z")
> [@Half\_Man\_Half\_Wit](#):
>
> [ol]
> [li]Suppose you have two boxes, A and B.[/li][li]Box A is filled with white marbles, and box B is filled with black ones.[/li][li]Both boxes are placed on a vibrating plate, such that the marbles in them bounce around.[/li][li]The walls of the boxes are removable.[/li][li]Suppose you put both boxes next to one another, and remove the now adjacent walls, creating one big box.[/li][li]Marbles from the white box A will bounce into the black box, and marbles from the black box B will bounce into the white box.[/li][li]There are more ways of realizing a state that’s pretty uniformly grey, than there are to realize a state that’s (say) all white in box A, and all black in box B.[/li][li]Consequently, there are more ways to go from a state that’s slightly inhomogeneous to one that’s more homogeneous, than there are ways to go to a state that’s even more inhomogeneous.[/li][li]To any observer who, as before, is only capable of seeing gross colors, the formerly black-and-white separated box will gradually tend to a shade of even gray.[/li][li]That observer might formulate a law, stating that black and white, if brought into contact, eventually even out to a uniform gray.[/li][li]Knowing the microscopic description, we know that this is just, again, a law of averages: there is nothing that prohibits, say, all or a sizable fraction of the white marbles from bouncing back into box A.[/li][li]Given a long enough timescale, the even grey will, eventually, separate into black and white patches.[/li][/ol]
>
> I expect greater resistance with this example. But again, try not to think ahead to the rest of this discussion; just consider the above system, as I have presented it. Do you agree that the conclusion is reasonable, here? That there is once again a law that appears valid thanks to the limited observations made at the macroscale, which we can see must be violated once we know about the microscopic level?
Actually I’m not sure if I agree with step 8 either. You can’t necessarily “go” from any arbitrary configuration of marbles to another, certainly not if you include a succession of three states in order.
~Max
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### Author:  [@Kent\_Clark](https://boards.straightdope.com/u/Kent_Clark)
#### Post date: [May 9, 2019, 12:45am UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/157 "2019-05-09T00:45:06Z")
> [@Chingon](#):
>
> It’s historical verbiage.
And we still call Pluto a “planet,” but science books have a big fat asterisk next to that.
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### Author:  [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)
#### Post date: [May 9, 2019, 4:34am UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/158 "2019-05-09T04:34:16Z")
> [@Max\_S](#):
>
> First I want to point out that the law from the coin example is not valid, was not formulated on a valid basis, and need not even appear to be valid. It is possible to observe greyness decreasing on a macroscopic scale in the previous example. The law was formulated nonetheless.
It’s formulated on exactly the same basis as every other law: by generalization from observational regularities. You do the coin example experiment a couple of hundred times, and you’ll always find the law to hold; absent knowledge of the microscopic dynamics, you have no justification to assume that in some cases, it’ll be violated. So it’s on exactly the same grounds as any other law of physics.
> [@](#):
>
> I take issue with step 9. I have no reason to believe the observer will observe a gradual change in color. You say the observer can only see gross color. If before he could distinguish two boxes of different colors, as soon as you remove the walls I take it he can only observe the combined box as a whole. Therefore the instant you remove the wall the observer sees flat grey.
>
> ~Max
Huh? How on Earth could that happen? The observer’s powers of observation are equal to the previous experiment; they’re able to perceive (what comes down to) the fraction of black vs. white marbles in a region, but not the actual marbles. This is really the same thing your computer screen does—by mixing three colors in different proportions, because you can’t see the individual pixels, different gross colors emerge, like in this [picture](http://www.huevaluechroma.com/pics/4-9.png). Or take something like this [ASCII art](https://i.pinimg.com/originals/03/4f/26/034f26abd1fbbe21c6c2fb58612e653a.jpg): the different grey regions are just different fractions of black, mixed with white. That’s the way the observer sees the system: the individual marbles are too small to be individually resolved, but different mixtures of them realize different levels of grey.
> [@Max\_S](#):
>
> Actually I’m not sure if I agree with step 8 either. You can’t necessarily “go” from any arbitrary configuration of marbles to another, certainly not if you include a succession of three states in order.
>
> ~Max
But that’s just counting. If there are more ‘more grey’ states than ‘less grey’ states, then a system in a ‘less grey’ state has more ways of evolving towards a ‘more grey’ state.
So assume some ‘less grey’ state G[sub]\<[/sub] can be realized by means of white and black marbles in ten different ways (corresponding to microstates G[sub]\<[/sub][sup]1[/sup] through G[sub]\<[/sub][sup]10[/sup]). Assume there are more ways to realize the ‘more grey’ state G[sub]\>[/sub] than there are ways of realizing the ‘even less grey’ state G[sub]\<\<[/sub]. Then, more of these ten states will evolve towards the more grey state than will evolve towards the less grey one.
Say there are eight states G[sub]\>[/sub][sup]1[/sup] through G[sub]\>[/sub][sup]8[/sup], and the states G[sub]\<\<[/sub][sup]1[/sup] and G[sub]\<\<[/sub][sup]2[/sup]. These are the states available from either of the states realizing G[sub]\<[/sub] on the next time-step. Then, eight out of ten times, if the system is in the state G[sub]\<[/sub], we will see it evolve into G[sub]\>[/sub]. (Perhaps it helps to recall, here, that a reversible evolution always takes different states to different states, as if it didn’t, i. e. by taking two different states to the same following state, you can’t tell which was the original state from looking at the later one, and thus, can’t reverse the evolution.)
Thus, at each time-step, we’re more likely to observe an increase in grey-ness, simply because there are more ways to get more grey.
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### Author:  [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)
#### Post date: [May 9, 2019, 4:35am UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/159 "2019-05-09T04:35:18Z")
> [@kunilou](#):
>
> And we still call Pluto a “planet,” but science books have a big fat asterisk next to that.
It’s the same with the second law of thermodynamics—textbooks generally point out that it’s only valid statistically.
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### Author:  [@Mijin](https://boards.straightdope.com/u/Mijin)
#### Post date: [May 9, 2019, 5:37am UTC](https://boards.straightdope.com/t/is-the-second-law-of-thermodynamics-routinely-violated/833151/160 "2019-05-09T05:37:41Z")
> [@Max\_S](#):
>
> But that’s just my point, assuming microscopic randomness or chaos means a particle can violate any number of laws. Not just the second law of thermodynamics.
It’s not about \*assuming \*randomness or chaotic behaviour, it’s that models that include these features make good predictions. e.g. we can predict very precisely the frequency with which electrons will tunnel through a barrier.
(OK, I know with “randomness” there’s a degree of interpretation involved and it’s possible there could be non-local hidden variables. **Half Man Half Wit** will know better than me.
But I’m not aware of any effort to interpret away _chaotic_ behaviour. Or anyone that claims it breaks physical laws.)
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