# 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

My question relates to whether the 2nd law of thermodynamics is a an empirical or mathematical law. If we can reason purely from the laws of statistics that entropy can only increase, then the 2nd law of thermodynamics cannot be falsifiable and therefore shouldn't be considered a scientific theory. On the other hand, if there is some empirical information that we require before concluding that entropy can only increase, then it is subject to refutation. But which is it?

PS. My goal is not to start a controversial or anti-scientific thread; I would be quite happy to get a simple and convincing answer. I'm aware from a quick Google search that people have argued the law is falsiable, but didn't find their reasoning convincing for reasons that I'd be happy to elaborate on.

The premise of this thread strikes me as bizarre. If we know why something is true, we should immediately declare it as unfalsifiable and therefore unscientific?

• Paul Colby, binis, russ_watters and 2 others
...shouldn't be considered a scientific theory.
It isn't a theory.

It's a Law.

That simply means 'we observe this to occur, predictably, under the right circumstances'. It does not say they can never be violated, so there's no issue of unfalsifiability.

Like Newtonian gravity, Galileo's square-cube law, Kepler's Laws of orbits**, the ideal gas laws, etc.

We don't even have to know why they work before being able to define them as laws. Kepler developed his laws of planetary motion several decades before Newton published his account of universal gravitation.

So, yes: empirical.

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• PORFIRIO I

"Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena.
...
Laws are developed from data and can be further developed through mathematics; in all cases they are directly or indirectly based on empirical evidence. It is generally understood that they implicitly reflect, though they do not explicitly assert, causal relationships fundamental to reality, and are discovered rather than invented."
https://en.wikipedia.org/wiki/Scientific_law

• Ranvaldo, binis, Leo Liu and 1 other person
If we can reason purely
I have isolated part of your question for a purpose. It tacitly assumes a state of grace we do not inhabit. As (I cannot believe I am quoting him) Donald Rumsfeld once said:

there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don't know we don't know. And if one looks throughout the history of our country and other free countries, it is the latter category that tend to be the difficult ones.

The power of the scientific method is that it has a chance to deal with all these classes of knowledge. There is always the third category.

• PhDeezNutz, Bystander and russ_watters
As (I cannot believe I am quoting him) Donald Rumsfeld once said:

there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don't know we don't know. And if one looks throughout the history of our country and other free countries, it is the latter category that tend to be the difficult ones.
That is such an awesome quote -- I don't think I've ever seen it before.
On the other hand, if there is some empirical information that we require before concluding that entropy can only increase, then it is subject to refutation. But which is it?
Surely you can, yourself, think of an experiment that could test and potentially falsity it... can't you?

• Dale and hutchphd
I don't feel as though the replies so far have addressed my question, which I'll admit may be due to a lack of clarity on my part. Let me have another go.

Consider two well-known "laws", Newton's law of gravity and the law of large numbers. According to Popper and his notion of falsifiability, The first is a scientific law, the second isn't; the first is falsifiable, but the second isn't. This is because the law of large numbers can be deduced purely from mathematical reasoning, whereas Netwon's law of gravity can't.

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.

• aliens123 and Stephen Tashi
Hm ... how many angels CAN dance on the head of a pin?

• Chestermiller

Did you read any of post 3 or 4?

I can "falsify" any law at any time simply by changing the parameters of the scenario. (That's not really what 'falsify' means, but therein lies the 'rub' of this thread).

Inside a hollow sphere, gravity doesn't make things fall.
A solar-orbiting satellite with a reflective sail won't sweep out equal areas in equal times.
A heterogeneous object won't have its mass cube as its cross section squares.
etc.

A law simply means "This is observed to occur predictably, under appropriate circumstances".
Note that it does not say 'this always occurs'.

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• Ranvaldo, russ_watters and phinds
...the law of large numbers ... isn't [falsifiable]. This is because the law of large numbers can be deduced purely from mathematical reasoning,
How does this follow?

How does mathematical deduction equate to unfalsifiability?

Consider two well-known "laws", Newton's law of gravity and the law of large numbers. According to Popper and his notion of falsifiability, The first is a scientific law, the second isn't; the first is falsifiable, but the second isn't. This is because the law of large numbers can be deduced purely from mathematical reasoning, whereas Netwon's law of gravity can't.

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.

I think there's two different things you're talking about here. One is about whether a mathematical formula/relationship can be falsifiable, the second is about how this formula or relationship applies to the real world. The 2nd law of thermodynamics, in terms of its mathematics, can't be falsified any more than ##a+b=c## can be falsified. Given certain inputs, you get a certain output according to the rules of mathematics. That's not falsifiable. Neither are the rules to baseball.

1. Does the concept itself apply to the real world.
2. How well these mathematical formulas describing this concept apply to the real world.

Number one is usually what we talk about as being falsifiable, and number two is what we use to determine if number one is false or not.

So yes. The 2nd law of thermodynamics can easily be falsified. There are a million ways to do so. In terms of being an empirical rather versus a mathematical law, it's obvious that this is an empirical law. One counter-example would prove that the 2nd law is not valid to the real world while doing nothing to the mathematics underlying it.

• Dale
I don't feel as though the replies so far have addressed my question, which I'll admit may be due to a lack of clarity on my part. Let me have another go.
Sigh. You didn't actually address any of the responses you were given. This does not make for productive conversation. I propose a test of the falsifiability of the following hypothesis: "The member madness is not interested in discussing his point, but rather is only interested in validation." Is my hypothesis falsifiable?
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.
Have you considered that the question may have more than one answer? Oops, I did it again. Let's add this to my hypothesis above.

• phinds
I will try again
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.
Suppose I bring to you a perpetual motion machine which powers a small LED light and you watch this continue for N years (N can be as large as you desire). This would do some violence to the second law. as we know it.
How can we "apply the same logic" to the law of large numbers...what is the experimental scenerio ??

• russ_watters

Did you read any of post 3 or 4?

I can "falsify" any law at any time simply by changing the parameters of the scenario. (That's not really what 'falsify' means, but therein lies the 'rub' of this thread).

...

A law simply means "This is observed to occur predictably, under appropriate circumstances".
Note that it does not say 'this always occurs'.

I explained in my second post why this is untrue. The law of large numbers is a mathematical law and doesn't require any empirical observations to establish. Mathematical deduction tells is 'this always occurs'. It is therefore unfalsifiable. You are speaking about a particular type of law, particularly ones which are inferred inductively from empirical evidence. My question is whether the 2nd law is such a law. From a statistical perspective, it looks to me like increase in entropy might be deducable from first principles.

How does this follow?

How does mathematical deduction equate to unfalsifiability?

This is 101 of falsifiability according to Popper. If something is mathematically guaranteed to be true, you can't falsify it. You can't falsify Euler's equation, nor can you falsify the law of large numbers.

I think there's two different things you're talking about here. One is about whether a mathematical formula/relationship can be falsifiable, the second is about how this formula or relationship applies to the real world. The 2nd law of thermodynamics, in terms of its mathematics, can't be falsified any more than ##a+b=c## can be falsified. Given certain inputs, you get a certain output according to the rules of mathematics. That's not falsifiable. Neither are the rules to baseball.

1. Does the concept itself apply to the real world.
2. How well these mathematical formulas describing this concept apply to the real world.

Number one is usually what we talk about as being falsifiable, and number two is what we use to determine if number one is false or not.

So yes. The 2nd law of thermodynamics can easily be falsified. There are a million ways to do so. In terms of being an empirical rather versus a mathematical law, it's obvious that this is an empirical law. One counter-example would prove that the 2nd law is not valid to the real world while doing nothing to the mathematics underlying it.

This is starting to feel a bit closer to a satisfactory answer. But what aspect of the mathematical formulation of the 2nd law could in theory not apply to the real world? If it is a law of statistics such as the law of large numbers, then I find it hard to envisage a physical universe where it could be violated. What kind of universe can violate the laws of statistics? As I mentioned in my previous post, I can imagine experiments which would falsify the law of large numbers, but I wouldn't call the law of large numbers a law of physics. Moreover, conceivability does not entail possibility, and so the cases where I imagine these laws being falsified could be logically impossible.

I will try again

Suppose I bring to you a perpetual motion machine which powers a small LED light and you watch this continue for N years (N can be as large as you desire). This would do some violence to the second law. as we know it.
How can we "apply the same logic" to the law of large numbers...what is the experimental scenerio ??

Suppose I randomly sample from the Gaussian distribution with zero mean N times (where N can be as large as you desire), yet the sample mean doesn't converge to zero sufficiently quickly. This would do some violence to the law of large numbers, as we know it.

The law of large numbers is a mathematical law and doesn't require any empirical observations to establish.

It does to prove that the law applies to reality. Of course, this is trivial, as our everyday lives tell us. We don't find that our coin flips are 80% heads or tails. Getting even deeper into it, we don't observe that gas molecules preferentially avoid one corner of the room instead of spreading out evenly as the law of large numbers tells us should happen, or that a car engine should suddenly start sucking in a 90/10% mix of air/fuel from the carburetor simply to due to statistical fluctuations in the fuel and air.

If we did observe such things then we would know that while the law of large numbers is proven mathematically, it doesn't accurately describe reality.

But what aspect of the mathematical formulation of the 2nd law could in theory not apply to the real world? If it is a law of statistics such as the law of large numbers, then I find it hard to envisage a physical universe where it could be violated.

I can't think of a way for the 2nd law not to work unless it is violated in such a minuscule way that it is immeasurable at this time. That is, if the entropy of an isolated system can decrease over time, it must do so as such a low rate that our current measurement devices and techniques are incapable of measuring it.

What kind of universe can violate the laws of statistics?

No idea. Large violations would produce a strange universe indeed.

The second law is not like the law of large numbers. It is also a little unusual as a physical law. Newton's second law is a differential equation consistent with many initial conditions. The second law of thermodynamics is a law about the initial conditions of the universe.

• binis and russ_watters
It does to prove that the law applies to reality. Of course, this is trivial, as our everyday lives tell us. We don't find that our coin flips are 80% heads or tails. Getting even deeper into it, we don't observe that gas molecules preferentially avoid one corner of the room instead of spreading out evenly as the law of large numbers tells us should happen, or that a car engine should suddenly start sucking in a 90/10% mix of air/fuel from the carburetor simply to due to statistical fluctuations in the fuel and air.

If we did observe such things then we would know that while the law of large numbers is proven mathematically, it doesn't accurately describe reality.

But we can take that reasoning to absurd limits, for example by applying the same logic to the laws of arithmetic. It's an empirical fact that if I put one apple and then another apple in a bowl then there are two apples in the bowl. We could imagine that I put one apple and then another in the bowl and there are three apples in the bowl, but that doesn't happen because the universe appears to obey the laws of arithmetic. Most wouldn't claim that the laws of arithmetic are scientific or falsifiable laws.

The second law is not like the law of large numbers. It is also a little unusual as a physical law. Newton's second law is a differential equation consistent with many initial conditions. The second law of thermodynamics is a law about the initial conditions of the universe.

If I'm not mistaken, the 2nd law is expected to hold regardless of the initial conditions. Entropy can never decrease according to the 2nd law (statistically speaking), and the fact that the initial conditions had low entropy then implies that we expect it to increase steadily over time. If the universe started at equilibrium state, entropy still wouldn't increase (statistically speaking again), which would again be in accordance with the 2nd law.

I think the OP has a good question. Falsifiable is a term I hear most often in connection with quantum interpretations. Unless and until an interpretation makes some prediction that can be observed to be true or false, it is not yet a candidate to become a "theory".

The 2nd law makes bold predictions. If the Hubble Telescope saw distant galaxies lined up to spell 42 (dot matrix style). That would be major news demanding explanation because the 2nd law predicts that won't happen spontaneously. If we did see 42, it would threaten to falsify the applicability of the 2nd law. But I'm not a fan of rigid definitions of words in natural language. For example, what is the mechanism to promote Einstein's relativity from theory to law? The time evolutions of the meaning and usage of words in natural language do not follow any rules.

Having said that, all the 2nd law says is that things evolve from less probable to more probable states. I would like to nominate the 2nd law for promotion to principle rather than just a mere law. Compare it to principles like causality, least action, cosmological. Principles are things we observe to be true always. Principles are not derived, nor do they require an explanation. We believe they are never violated. For example, travel back in time would violate causality. When we use our telescope, the 2nd principle says that we have never seen spontaneous arrangements like 42 in the cosmos, nor do we expect to see that ever.

• Stephen Tashi
Maybe the 2nd law (entropy increases as time passes) is more a tautology, since we could say "the future is the direction in time having a higher entropy"

• Stephen Tashi
But we can take that reasoning to absurd limits, for example by applying the same logic to the laws of arithmetic. It's an empirical fact that if I put one apple and then another apple in a bowl then there are two apples in the bowl. We could imagine that I put one apple and then another in the bowl and there are three apples in the bowl, but that doesn't happen because the universe appears to obey the laws of arithmetic. Most wouldn't claim that the laws of arithmetic are scientific or falsifiable laws.
You haven't said anything profound here, and while you seem to understand the issue just fine, you seem to be rejecting that understanding. This concerns me given that your main question is regarding the second law of thermodynamics.

I'll repeat what others have said, for emphasis: a purely mathematical relation in a mathematical space is not a statement about reality. 1+1=2 is not a statement about reality. It's not a belief. It isn't that it isn't falsifiable; falsifiability simply doesn't apply. It's true because we've declared it to be true.

1 apple + 1 apple = 2 apples is a statement about reality people believe to be true. It is an application of that mathematical relation/definition to reality. The fact that 1 apple + 1 apple = 2 apples is observed to be true does not mean 1+1=2 is generally true as applies to reality. I'm sure if you tried, you could think of plenty of examples where a naive application of 1+1=2 fails in reality. 1 atom + 1 atom = 1 atom, for example.

The second law of thermodynamics is clearly a statement about physical reality, not a strictly mathematical relationship. Clearly, falsifiability applies.

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• Ranvaldo, Dale, Drakkith and 1 other person
Maybe the 2nd law (entropy increases as time passes) is more a tautology, since we could say "the future is the direction in time having a higher entropy"
That's a definition of the thermodynamic arrow of time, not a statement about the accuracy of the 2nd law.

The second law of thermodynamics is a law about the physical quantity entropy. It is exactly as falsifiable as other physical laws: repeatedly measure the physical quantities in question and check whether the outcomes are compatible with the law which relates them. So just repeatedly measure the entropy of isolated systems and check if you find decreases.

Statistical mechanics tries to derive the macroscopic laws of thermodynamics from the microscopic dynamics and the mathematical laws of probability. In statistical mechanics, statements like the second law are theorems, i.e. they follow logically from a set of fundamental postulates / assumptions (like the fundamental postulate which relates probability and physics, or assumptions about the nature of the microscopic building blocks and their interactions). If the second law was falsified experimentally, we would conclude that at least one of these assumptions doesn't hold in the real word.

The second law is notable because its irreversibility is in tension with the time reversal symmetry of the microscopic equations. In his derivation, Boltzmann introduced a time asymmetry by hand (see his molecular chaos assumption). The question is still relevant today. In QM, for example, we have a similar tension between irreversible measurements and time-reversible microscopic equations of motion in the absence of measurements.

• Stephen Tashi, atyy, Dale and 1 other person
Statistical mechanics tries to derive the macroscopic laws of thermodynamics from the microscopic dynamics and the mathematical laws of probability. In statistical mechanics, statements like the second law are theorems, i.e. they follow logically from a set of fundamental postulates / assumptions (like the fundamental postulate which relates probability and physics, or assumptions about the nature of the microscopic building blocks and their interactions). If the second law was falsified experimentally, we would conclude that at least one of these assumptions doesn't hold in the real word.

I find this to be a fairly satisfying answer. It would be interesting to dig a bit further and investigate what those postulates themselves say, which of them are falsifiable, and what kind of universe would be consistent with a scenario in which they were false. For example, your link to the fundamental postulate says :

For an isolated system with an exactly known energy and exactly known composition, the system can be found with equal probability in any microstate consistent with that knowledge.

So if we lived in a universe in which some microstates were inherently more likely than others for a given macrostate, then the 2nd law of thermodynamics might not necessarily hold. I wonder if one could come up with a set of microphysical laws that would produce such a scenario, assuming that the universe if fully described by those microphysical laws. I find it hard to picture how that could work!

the universe appears to obey the laws of arithmetic. Most wouldn't claim that the laws of arithmetic are scientific or falsifiable laws

The laws of arithmetic themselves are not falsifiable; they are mathematical statements.

The observation that the universe appears to obey the laws of arithmetic is, on the other hand, a scientific, falsifiable statement; we could have observed that the universe did not obey the laws of arithmetic.

• etotheipi, A.T. and russ_watters
...we could have observed that the universe did not obey the laws of arithmetic.
We probably would have made up different laws of arithmetic in such a universe. We can also easily make up some arithmetic that our universe doesn't obey.

• russ_watters
So if we lived in a universe in which some microstates were inherently more likely than others for a given macrostate, then the 2nd law of thermodynamics might not necessarily hold. I wonder if one could come up with a set of microphysical laws that would produce such a scenario, assuming that the universe if fully described by those microphysical laws. I find it hard to picture how that could work!

PF routinely rejects questions about hypothetical universes in PF. Our mission is to discuss mainstream science, and that means this universe. You are asking, "What would the laws of physics be if the laws of physics were different?"

PF routinely rejects questions about hypothetical universes in PF. Our mission is to discuss mainstream science, and that means this universe. You are asking, "What would the laws of physics be if the laws of physics were different?"

That's their prerogative. Asking whether a law is falsifiable is equivalent to asking whether there exists a possible universe in which the law doesn't hold (as cached out rigorously by Kripke in his modal logic https://plato.stanford.edu/entries/logic-modal/). As pointed out by a previous poster, the 2nd law of thermodynamics is a theorem of certain postulates, so that disproving the 2nd law is equivalent to disproving one (or several) of those postulates. Thus, if the 2nd law is falsifiable then we have to accept the possibility of a universe which violates one of those postulates.

But we can take that reasoning to absurd limits, for example by applying the same logic to the laws of arithmetic. It's an empirical fact that if I put one apple and then another apple in a bowl then there are two apples in the bowl. We could imagine that I put one apple and then another in the bowl and there are three apples in the bowl, but that doesn't happen because the universe appears to obey the laws of arithmetic. Most wouldn't claim that the laws of arithmetic are scientific or falsifiable laws.

Indeed. As Russ already explained, the rules of arithmetic aren't falsifiable, but their application to the real world is.

Asking whether a law is falsifiable is equivalent to asking whether there exists a possible universe in which the law doesn't hold (as cached out rigorously by Kripke in his modal logic https://plato.stanford.edu/entries/logic-modal/).
Thus, if the 2nd law is falsifiable then we have to accept the possibility of a universe which violates one of those postulates.

I disagree entirely. I am under no obligation to accept the possibility of real, alternate universes.

• Dale, hutchphd, DaveC426913 and 1 other person
It's an empirical fact that if I put one apple and then another apple in a bowl
Most of the time. Not all of the time. Sometimes you get apple sauce. Other times you get an apple tree. Our universe does not feature a law of conservation of apples.

• russ_watters
I disagree entirely. I am under no obligation to accept the possibility of real, alternate universes.

That was never suggested. The existence of a possible universe and a real universe are two different things. Falsifiability requires the logical possibility that an alternative universe could have existed. Modal logic is the formalisation of those kinds of analyses.

Asking whether a law is falsifiable is equivalent to asking whether there exists a possible universe in which the law doesn't hold...
[separate post]
Falsifiability requires the logical possibility that an alternative universe could have existed.

Thus, if the 2nd law is falsifiable then we have to accept the possibility of a universe which violates one of those postulates.
No it isn't/doesn't. Finding out that we're wrong about how this universe works tells us nothing whatsoever about the possible existence of another universe or what its laws might be. It's just a self-contained logical construct. Similarly, writing 1+1=3 does not suggest the possibility that another universe exists where putting two apples in a basket yields three apples.

• Ranvaldo
That was never suggested. The existence of a possible universe and a real universe are two different things. Falsifiability requires the logical possibility that an alternative universe could have existed. Modal logic is the formalisation of those kinds of analyses.

Then may I ask that you be clear with your use of the word 'universe' then? Right now I don't know what your distinction is between 'possible universe' and 'real universe'. If we are discussing some kind of alternative universe that can't be real then I see no point in the discussion.

• russ_watters
No it isn't/doesn't. Finding out that we're wrong about how this universe works tells us nothing whatsoever about the possible existence of another universe or what its laws might be. It's just a self-contained logical construct. Similarly, writing 1+1=3 does not suggest the possibility that another universe exists where putting two apples in a basket yields three apples.

I'm finding it hard how to understand how you got these ideas from what I wrote. What I said was the the statement "X is falsiable" is equivalent to the statement that "it is possible that X doesn't hold". In the language of modal logic this is typically phrased as "there is a possible world in which X does not hold". Nothing about this entails the metaphysical reality of alternative universes. Moreover, even in the restricted sense of possible worlds that was intended re modal logic, an observation in this world still wouln't update our beliefs about which alternative worlds are possible. Finally, why would writing 1+1=3 suggest the possibility of another universe exists where putting two apples in a basket yields three apples?

Then may I ask that you be clear with your use of the word 'universe' then? Right now I don't know what your distinction is between 'possible universe' and 'real universe'. If we are discussing some kind of alternative universe that can't be real then I see no point in the discussion.

I can provide some references if it helps, but my feeling is that the discussion had become somewhat sidetracked at this point. They are essentially introduced in a system of formal logic (modal logic) to rigorously define notions of "possibility" and "necessity" and to allow logical inferences to be made on the basis of those kinds of propositions. They were famously used by Saul Kripke (https://en.wikipedia.org/wiki/Saul_Kripke) who used them ask questions about whether statements such as "water is H20" are necessarily or contingently true in his book Naming and Necessity.

https://en.wikipedia.org/wiki/Possible_world
https://plato.stanford.edu/entries/possible-worlds/

Asking whether a law is falsifiable is equivalent to asking whether there exists a possible universe in which the law doesn't hold
That is not even remotely what it means. Falsifiable means that there exists a possible experiment in this universe where a specific outcome would mean the law is false.

The 2nd law is immensely falsifiable. Take any isolated system, measure the entropy over time, if it decreases then the law is falsified. E.g. if a temperature gradient appears, if a dye un diffuses in a fluid, if an egg unscrambles, etc. Any of those outcomes would falsify the 2nd law. So it is falsifiable and hence scientific.

• russ_watters