# Is the Second Law of Thermodynamics Falsifiable?

In summary, the 2nd law of thermodynamics is a law that describes the tendency of entropy to increase.f
Logical possibility has nothing whatever to do with the possibility that the second law might not hold in our universe. Our universe is not the only logically possible universe; plenty of things that are logically possible are impossible in our universe.

I don't follow your argument. My claim is that logical possibility constrains the facts which can be falsified (in any universe). Facts which hold in all logically possible worlds are called necessary truths, and are not generally considered falsifiable.

My claim is that logical possibility constrains the facts which can be falsified

Yes, tautologies cannot be falsified because they are true in all logically possible worlds. But, as has already been pointed out, the second law is not a tautology. Tautologies are statements that are derivable from the laws of logic and the definitions of terms alone. "All squares have 4 sides" is such a statement, because having 4 sides is part of the definition of a square. Any tautology must therefore be consistent with all other logically possible statements. But the second law is not: it is inconsistent with the logically possible observation statement described in post #61. So the second law is not a tautology, and there are logically possible worlds in which it is not true.

Others have claimed that the 2nd law of thermodynamics can be derived from probability alone.

I haven't claimed that, and I'm not sure that "can be derived from probability alone" is equivalent to "is a tautology" anyway.

I don't follow your argument. My claim is that logical possibility constrains the facts which can be falsified (in any universe). Facts which hold in all logically possible worlds are called necessary truths, and are not generally considered falsifiable.
If the second law follows directly from the statistics of random motions of atoms, then your assumption is that the motions of atoms are random. The second law would be falsified if atomic motions were found not to be random.

Yes, tautologies cannot be falsified because they are true in all logically possible worlds. But, as has already been pointed out, the second law is not a tautology. Tautologies are statements that are derivable from the laws of logic and the definitions of terms alone. "All squares have 4 sides" is such a statement, because having 4 sides is part of the definition of a square. Any tautology must therefore be consistent with all other logically possible statements. But the second law is not: it is inconsistent with the logically possible observation statement described in post #61. So the second law is not a tautology, and there are logically possible worlds in which it is not true.

I did mention in my earlier reply that I have more or less been convinced already by the arguments in this thread that the 2nd law is falsifiable. In particular that there appears to exist logically consistent physical theories that would violate it. Rather than continuing to argue over that point, I was hoping to refine the question to get a better understanding of what kinds of logically possible worlds might violate the 2nd law. It seems to me that the 2nd law does logically follow from a very minimal set of quite general assumptions (as suggested by a previous post regarding its derivation from probability). What are the assumptions needed to derive the 2nd law from pure probability theory? If it is not a tautology, is that because probability theory is not tautological, or because something else is required in addition to the laws of probability?

What are the assumptions needed to derive the 2nd law from pure probability theory?

Basically, that the system is closed, that all microstates of the system are equally probable, and that we are using a coarse-graining of microstates into macrostates that leads to the existence of a thermodynamic equilibrium state which has so many more microstates than any other macrostate that the probability is overwhelming that a randomly chosen microstate of the system will be in the thermodynamic equilibrium macrostate.

If it is not a tautology, is that because probability theory is not tautological, or because something else is required in addition to the laws of probability?

Probability theory as a piece of pure math is tautological (since any piece of pure math is), but as a piece of pure math it doesn't apply to anything.

Probability theory as applied to any actual physical system is not tautological, because it must be supplemented with propositions describing the actual physical system that can be logically linked to probability theory.

Others have claimed that the 2nd law of thermodynamics can be derived from probability alone.
So what? Who cares how it is derived in determining falsifiability. It is logically possible that the world does not obey the laws of probability. I don’t see how the method of derivation matters to falsifiability. Per the definition of falsifiable it is falsifiable, as described above.

Furthermore, I disagree that the second law of thermo can be derived from statistical mechanics. Statistical mechanics can derive that the second law is asymptotically correct over long times and for large systems. The second law itself does not say “entropy doesn’t decrease in the long run for large systems” it just says “entropy doesn’t decrease”. So in fact the “derivations” you suggest actually indicate that the second law will occasionally be falsified for sufficiently small systems over sufficiently short time scales. In this sense, statistical mechanics supersedes and generalizes the second law of thermo, just like relativity supersedes and generalizes Newtonian mechanics.

In the same way that the law "all squares have 4 sides" is clearly falsifiable according to sentence you selected.
I am still interested in hearing how you think this is falsifiable. What observation would be inconsistent? I think you are misapplying the definition.

If you observe a three sided object, then that is a triangle, so observation of a three sided object does not falsify it. So what observation would falsify it?

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russ_watters
Basically, that the system is closed, that all microstates of the system are equally probable, and that we are using a coarse-graining of microstates into macrostates that leads to the existence of a thermodynamic equilibrium state which has so many more microstates than any other macrostate that the probability is overwhelming that a randomly chosen microstate of the system will be in the thermodynamic equilibrium macrostate.

Depending on how one defines things, this need not be considered "pure" probability, since the assumption that all microstates of the system are equally probable need not hold for all dynamical systems. For example, it is not clear if the assumption holds when the dynamical system is not ergodic. It may be possible that the second law holds without ergodicity, but that possibility seems not yet well understood. I found an interesting discussion in Ergodic hypothesis in classical statistical mechanics by César R. de OliveiraI and Thiago Werlang.

Here are some other interesting discussions:
https://arxiv.org/abs/1503.07538 (see Chapter 7 and Appendix A)
p56: "We have seen that the ETH as defined in Definition 3 is by construction essentially sufficient and, in a certain sense, necessary for thermalisation. The necessary part, however, only holds if one is willing to call a system thermalising only if it thermalises for a given set of POVMs for all initial states with a sufficiently narrow energy distribution for which it also apparently equilibrates. Hence, there is the possibility to show thermalisation in systems that do not fulfil the ETH, if one is willing to restrict the class of allowed initial states. As we will see in the following this can indeed be done."

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I am still interested in hearing how you think this is falsifiable. What observation would be inconsistent? I think you are misapplying the definition.

If you observe a three sided object, then that is a triangle, so observation of a three sided object does not falsify it. So what observation would falsify it?

It is only falsifiable according to your own mistaken definition that " there is a set of singular observation sentences which falsifies (i.e., is inconsistent with) Σ " which you subselected without including the broader requirement of logical possibility. According to my own definition the statement is not falsifiable because one has to not only name a possible observation but has also to verify whether the observation is logically possible. You seem to have no problem applying the correct definition, and you just did so in this post.

My question is which kind of "law" is the 2nd law of the thermodynamics? And pointing out a case in which we can imagine the 2nd law being falsified won't work, as we can apply the same logic to other statistical laws, including the law of large numbers.

Sir Arthur Stanley Eddington in “THE NATURE OF THE PHYSICAL WORLD” (Cambridge, At the University Press (1929)):

Primary and Secondary Law. I have called the laws controlling the behaviour of single individuals "primary laws”, implying that the second law of thermodynamics, although a recognised law of Nature, is in some sense a secondary law. This distinction can now be placed on a regular footing. Some things never happen in the physical world because they are impossible; others because they are too improbable. The laws which forbid the first are the primary laws; the laws which forbid the second are the secondary laws…..

….But for all its completeness primary law does not answer every question about Nature which we might reasonably wish to put. Can a universe evolve backwards, i.e. develop in the opposite way to our own system? Primary law, being indifferent to a time direction, replies, "Yes, it is not impossible". Secondary law replies, "No, it is too improbable". The answers are not really in conflict; but the first, though true, rather misses the point.

Ranvaldo, hutchphd and vanhees71
It is only falsifiable according to your own mistaken definition
I don’t think it is falsifiable even with that definition (which isn’t mine, it is Hempel and Popper’s according to your source). What observation can be made to falsify it? You can write down the sentence “square with three sides” but the definition requires an “observation sentence” not merely a “sentence”. There is no observation you can make which corresponds to that sentence, so it isn’t an observation sentence.

If you disagree then spell out the actual observation. What combination of observed lengths and angles leads to a falsification?

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I don’t think it is falsifiable even with that definition (which isn’t mine, it is Hempel and Popper’s according to your source). What observation can be made to falsify it? You can write down the sentence “square with three sides” but the definition requires an “observation sentence” not merely a “sentence”. There is no observation you can make which corresponds to that sentence, so it isn’t an observation sentence.

If you disagree then spell out the actual observation. What combination of observed lengths and angles leads to a falsification?

You quoted a small part of the definition attributed to Hempel and Popper but left out the part that stated the observation must also be logically possible. You now appear to have resorted to defining observation sentence to mean "sentence pertaining to an observation which is also logically possible", which is the same as my definition anyway. In fact, that isn't the definition of an observation sentence.

https://plato.stanford.edu/entries/quine/#ObseSent

In fact, that isn't the definition of an observation sentence.
So what is? I had encouraged you by PM to provide all of the definitions of the unfamiliar terms. I am not trying to cherry-pick a definition, but the one that I picked had the least unfamiliar terminology.

You quoted a small part of the definition attributed to Hempel and Popper but left out the part that stated the observation must also be logically possible.
I quoted the whole part you quoted. If you provided an incomplete reference that is on you.

I quoted the whole part you quoted. If you provided an incomplete reference that is on you.

That's simply false. I boldfaced the statement on logical possibility in the quote I posted and you left it out.

That's simply false. I boldfaced the statement on logical possibility in the quote I posted and you left it out.
That wasn’t part of the definition. It was a subsequent explanatory paragraph! Look at it. There is the definition I quoted, then the statement that the previous sentence is the one used by Popper. Then the subsequent explanation. That is not part of the definition.

In any case, I just read the link on observation sentences and it completely corroborates my assertion. Your “observe a 3 sided square” is not an observation sentence. There is no set of sensory stimuli that correspond to it.

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In any case, I just read the link on observation sentences and it completely corroborates my assertion. Your “observe a 3 sided square” is not an observation sentence. There is no set of sensory stimuli that correspond to it.

And how did you arrive at that conclusion? Presumably by noting that the observation would be logically impossible. Or put another way, that there is no logically possible world in which the observation could occur.

A justification for the assertion that such the observation suggested in post #61 is logically possible.

Logic is only as good as the assumptions or givens. A logical deduction about a proposed experiment on a system is only as good as the givens assumed. If the givens are garbage, so is the logical conclusion one has made. If the system in #61 doesn't conform to the assumptions one is making about it, then it's the assumptions which must be changed. Hence the experiment has falsified the assumptions or the model of said system.

And how did you arrive at that conclusion?
By noting that “I observe a three sided square” is not an observation sentence since it does not correspond to any sensory stimulus or combination of sensory stimuli. As I already said.

If you disagree then spell out the actual observation. What combination of observed lengths (ruler observations) and angles (protractor observations) leads to a falsification?

Purely by Poppers definition the second law is falsifiable and your straw man is not.

By noting that “I observe a three sided square” is not an observation sentence since it does not correspond to any sensory stimulus or combination of sensory stimuli. As I already said.

And how did you come to know that “I observe a three sided square” "does not correspond to any sensory stimulus or combination of sensory stimuli"? Presumably you will admit that “I observe a four sided square” does correspond to a sensory stimulus? And yet the difference between the two sentences can only deduced from logical considerations.

And how did you come to know that “I observe a three sided square” "does not correspond to any sensory stimulus or combination of sensory stimuli"? Presumably you will admit that “I observe a four sided square” does correspond to a sensory stimulus? And yet the difference between the two sentences can only deduced from logical considerations.
If we are arguing about the meaning of threeness or fourness then we are not arguing about universes. We are arguing about words.

If we are arguing about what it entails for an object to have three sides or four sides, we are not arguing about the problem at hand. We are arguing about definitions.

Once we have dispensed with details of interpretation, there is no physical problem remaining. All that remains is a dispute about whether three is equal to four. Or whether four is equal to four. We need not invoke universes to argue that. [In my view, "three" is part of the model, not part of the universe].

russ_watters
how did you come to know that “I observe a three sided square” "does not correspond to any sensory stimulus or combination of sensory stimuli"?

Because having four sides is part of the definition of a square, as has already been pointed out.

Because having four sides is part of the definition of a square, as has already been pointed out.

Exactly, which is equivalent to saying that the observation can't occur because it's logically impossible.

Presumably you will admit that “I observe a four sided square” does correspond to a sensory stimulus?
The relevant observation sentence would be eg “I observe four straight connected line segments each of 1 m length by ruler with four 90 degree interior angles by protractor”. That is the sensory stimulus, a series of observable measurements.

There are no such observation statements that correspond to your straw man. So just purely by Poppers definition the second law is falsifiable and your straw man is not. There is no need to add the additional language. Poppers definition is sufficient on its own.

In this case it is true that the reason there is no observation sentence is because of logical impossibility. But the reason is not necessary for the definition, merely the fact that there is no such observation sentence.

There are other situations where there is no observation sentence and the reason has nothing to do with logic. For example, the Lorentz aether is perfectly logically possible but is designed so that there is no observation sentence that can be attributed to it. The Lorentz aether is therefore non-falsifiable, but logically possible. So the key is the existence or non-existence of observation sentences, not logical possibility or impossibility.

Importantly, I was not quoting out of context nor twisting words. I was correctly applying the quoted definition to reach the clear conclusion that the 2nd law is falsifiable and the straw man is not. So your posts 62 and 79 are wrong.

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russ_watters
The relevant sensory stimulus would be eg “I observe four straight connected line segments each of 1 m length by ruler with four 90 degree interior angles by protractor”. That is the sensory stimulus, a series of observable measurements.

This line of argument equates to denying that the original statement was an observation statement. An observation statement is taken to be a statement about sense experiences that can be directly used for falsification, and which does not require to be further decomposed into simpler sensory stimuli to be applied. Quine used examples such as "the cat is on the mat", but he emphasised the requirement of intersubjective agreement on the utterance within a community of speakers. If (as you appear to argue) "I see a four sided square" isn't already sufficient to define the observation, then it's not an observation statement. But that's not how the term was intended, at least by Quine, and "I see a four sided square" is already good enough as is. If anything, the reason "I see a 4 sided square" would be considered an observation statement while "I see a 3 sided square" would not is that there would not be intersubjective agreement among the community of speakers in the latter case. At least according to the definitions in the source below.

Source: https://www.jstor.org/stable/pdf/42969075.pdf?refreqid=excelsior%3A17843ed1c85feac7ab9dc15b66cc5f5d

"Such, then, is an observation sentence: it is an occasion sentence whose occasion is not only intersubjectively observable but is generally adequate, moreover, to elicit assent to the sentence from any present witness conversant with the language. (Quine (1975a) p. 73)"

" A person p understands the observation sentence s if and only if there is unique set of stimulations such that p and every speaker of the same language as p would assent to s, when asked s in the presence of any member of this set and would dissent from s when asked s in the presence of no member of the set. "

The reason why you don't see someone flip a coin ten times, and heads every time, is because that is a small percentage of allowed outcomes. The reason why you don't get a royal flush when playing poker is because it is a small percentage of allowed outcomes. The reason why you don't see the air rush to the corners of the room is because trajectories of air molecules that lead to that configuration are a small percentage of allowed trajectories. Of course, it is possible in all these cases. Of course, it possible to flip a coin ten times in a row, and get heads every time. If you flip a coin enough times, it is guaranteed to happen. Of course, it is possible to get a royal flush while playing poker. Of course, it is possible for the air to rush to the corners of the room. If you wait long enough, it is guaranteed to happen. It is possible for entropy to decrease. It is possible for the Second Law of Thermodynamics to be violated.

In Renaissance Europe, they had absolute monarchy and the divine right of kings. The laws were not the result of any legislative process. Laws were simply decreed by the king. You were not allowed to debate whether the laws could be different or ask why they are the way they are, because that would be questioning the will of the king. It was assumed that the laws must always be followed since to imply otherwise was treason punishable by death.

In Renaissance Europe, they made an analogy between a country and the Universe, and the king and God. Whatever a scientist's private beliefs, they had to at at least publicly pretend that their goal was to gain insight into God's will. Natural laws were simply decided by God. You were not allowed to debate whether the laws could be different or ask why they are the way they are, because that would be questioning the will of God. It was assumed that the laws must always be followed since to imply otherwise was blasphemy punished by eternal damnation. This analogy is the reason for the use of the word "laws" in physics. It was assumed that all "laws" were sacred, and that "laws" in physics must always be true.

This changed in the 19th Century. Government shifted from absolute monarchy to parliamentary democracy. Science became more secular, and openly contradicted the church with such things as the age of the Earth, or evolution. It was also recognized that so-called laws in physics were not always true. You were allowed to ask why laws were true, or usually true, or under what circumstances, they were true. We now know that many laws are not always true. For example, Ohm's law does not apply to non-linear elements, such as diodes. With this new way of thinking, we quit using the word "law". This is why we say "Maxwell's laws" but do not say "Einstein's laws" when referring to the various equations discovered by Einstein. However, in physics. we do not change the names of things. We are not going to stop using the name "Maxwell's laws" and start calling them "Maxwell's equations". If you hear someone calling something a "law" in physics, it is only because they referring to something that was named before we quit using the word "law".

he emphasised the requirement of intersubjective agreement on the utterance within a community of speakers
And there is no such agreement for “I observe a three sided square”. So again Poppers definition is sufficient and your posts 62 and 79 are wrong.

And there is no such agreement for “I observe a three sided square”. So again Poppers definition is sufficient and your posts 62 and 79 are wrong.

Yep, that's what I wrote. But your posts are also wrong :P

Yep, that's what I wrote. But your posts are also wrong :P
Which one? Certainly not my 61.

Which one? Certainly not my 61.

Specifically certain claims in most of the posts you made from 85 onwards, that an observation sentence needs to spell out a set of sensory stimuli to be valid. I had conceded openly a few times and long ago that I had become convinced the 2nd law was falsifiable, as you claim in 61.

Also, it still seems to me that the only way we know there couldn't be intersubjective agreement by a community of speakers regarding the statement "I see a square with 3 sides", is that it is logically impossible. So as far as I can see, my reasoning was correct.

Also, it still seems to me that the only way we know there couldn't be intersubjective agreement by a community of speakers regarding the statement "I see a square with 3 sides", is that it is logically impossible.
So as far as I can see, my reasoning was correct.
Your reasoning is incorrect because the logical impossibility is not relevant, only the fact that there is no observation sentence is relevant. As I showed in post 93.

At this point this has become unproductive. This thread is closed again.