In the thread on Dualism, it was claimed that [POST=21610420]we have observed violations[/POST] of the second law of thermodynamics; it was even suggested that [POST=21612451]large-scale violations occure with relative frequency[/POST]. My response is that we have not observed violations, and that a single violation of the second law would result in a paradigm shift for many fields of science.
There are multiple formulations of the second law of thermodynamics. These are formulations of the same law as I was taught early on in secondary school[1][2]:
There is also an axiomatic formulation by Constantin Carathéodory[3][4]:
Wikipedia says Carathéodory’s formulation is incomplete without adding the following, although I cannot access the source or a translation[5][6]:
[1] Clausius, M. R. (1856, August). On a modified Form of the second Fundamental Theorem in the Mechanical Theory of Heat. London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, Series 4, 12(77), 86. Retrieved from London, Edinburgh and Dublin Philosophical Magazine and Journal of Science : Free Download, Borrow, and Streaming : Internet Archive
[2] Thomson, W. (1853). On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule’s equivalent of a Thermal Unit, and M. Regnault’s Observations on Steam. Transactions of the Royal Society of Edinburgh, 20(2), 265. Retrieved from https://digital.nls.uk/scientists/archive/74629508
[3] Carathéodory, C. (1909, September). Untersuchungen über die Grundlagen der Thermodynamik. Mathematische Annalen, 67(3), 363. https://doi.org/10.1007/BF01450409
[4] Caratheodory, C. (n.d.). Examination of the foundations of thermodynamics [PDF file]. (D. H. Delphenich, Trans.) Retrieved from http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf (Original work published 1909).
[5] Second law of thermodynamics. (n.d.). In Wikipedia. Retrieved April 27, 2019, from Second law of thermodynamics - Wikipedia
[6] Planck, M. (1926) Über die Begründung des zweiten Hauptsatzes der Thermodynamik. Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse, 1926, 453-463.
I’ve only heard of “adiabatic” in reference to a system where heat does not leave the system, and that was the meaning I used.
If you are describing a system consisting of a 5000K star orbiting an 8000K star, and you allow radiation to “leave” the system, then the second law of thermodynamics as formulated by Carathéodory (and Planck) does not apply. It is not violated; it does not apply to the system you have described.
If however, you include the surrounding space in the system, extending to infinity and encompassing all radiation emitted, then the second law of thermodynamics holds true.
At any reasonable macroscopic level, the 2nd law of thermodynamics has never been demonstrated to be violated, experimentally or theoretically. At the microscopic level, where statistical probability is potentially, locally, over very short times, superseded by quantum mechanical effects, it is possible to view some systems as violating the second law (though it it not clear to me that experimentally it is possible to create a completely isolated system as required by the second law, given the extent of the quantum field).
You should never take your scientific knowledge from blithe pronouncements in a thread on philosophy. Philosophers, apparently, can’t be bothered to add in all the caveats and conditions that go along with the"violation" of a scientific principle.
Quantum theory doesn’t enter into it. For any system of N particles, there’s a probability scaling with 1/sqrt(N) that violations of the second law will be observed. For any macroscopic system, that probability is so low as to be completely negligible, while for systems of few constituents (which we can take to be classical), violations can and do occur.
Entropy is fundamentally a measure for how many microstates (unobservable individual particle arrangements, say) lead to the same macrostate (the gross, macroscopic properties of a system). So, there are many more microstates corresponding to all of the gas in a room being evenly distributed, than there are corresponding to all the gas bunching up in the middle; hence, the former is a high-entropy state, while the latter is a low-entropy state.
If you start out with a low-entropy configuration, any given change is likely to lead to a higher-entropy configuration, just by virtue of how many more ways there are to increase entropy, than to decrease it. But that doesn’t mean that spontaneous decreases of entropy are impossible; it merely means that they’re unlikely.
Take a toy system of three ‘particles’, 1, 2, and 3, carrying one unit of energy each, which can be in each of three boxes A, B, and C. This gives us the following ten distinguishable macrostates:
[ul] li Even distribution: each box contains one particle[/li]li Box A contains two particles, B one, C none[/li]li Box A contains two particles, B none, C one[/li]li Box A contains one particle, B two, C none[/li]li Box A contains no particle, B two, C one[/li]li Box A contains one particle, B none, C two[/li]li Box A contains no particle, B one, C two[/li]li Box A contains all three[/li]li Box B contains all three[/li]li Box C contains all three[/li][/ul]
We can compute the probability of each macrostate, by counting the number of microstates that realizes it. The first macrostate can be realized by every permutation of particles, distributed over the boxes, thus, there are 3! = 6 possible ways to realize it. The last three macrostates can be realized in exactly one way. The six remaining cases can each be realized in three different ways (e. g. for (A2B1C0), particles 1 and 2, 1 and 3, or 2 and 3 could be in box A, the remaining one in box B).
In total, we thus have 6 + 6 * 3 + 3 * 1 = 27 possible microstates (which of course we knew, since there are 3 * 3 * 3 possibilities to distribute 3 objects among 3 boxes). Now, we can calculate the probabilities for each macrostate, as well as their entropy (as the natural logarithm of the number of ways in which it can be realized, i. e. the microstates):
Assuming a simple dynamics of particles just hopping to a random box at each time step, we see that, while it’s more likely for entropy to increase with each step, it’s by no means impossible for it to decrease, as well. Starting out in one of the lowest entropy states, the probability that the next timestep will lead to a higher entropy state is 24 / 27 ~ 89%, with an 11% chance of staying the same. An intermediate-entropy state has an 11 % chance of decreasing entropy (and thus, violating the second law, as a colder box will transfer energy to an already hotter one, say in the transition (A0B1C2) –> (A0B0C3)), a 22% change of increasing, and a 67% chance of remaining equal.
As you increase the size of the system, these probabilities will favor higher entropy states ever more strongly. Still, if you wait long enough, you will observe violations of the second law even there—it’s just that the wait time will quickly exceed even cosmological timescales.
By assuming the particles are “hopping to a random box” you have assumed the conclusion. The second law of thermodynamics specifically contradicts such a process.
No. Any other dynamics would work just as well, as long as all microstates are equally probable.
Really, none of this is controversial in the slightest. Every physics student learns it in a course on statistical mechanics. People have even used this to try and argue that the universe itself might be due to a spontaneous fluctuation from a high-entropy state into a low-entropy state:
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I always thought thermodynamic equilibrium was when two systems are in contact with no net flow of energy (heat). By allowing for microstatic particles to randomly reconfigure into distinct macrostates, you have also defied thermodynamic equilibrium.
Even the kinetic theory, to my knowledge, only allows for random movements so long as they express the same macrostates. But I might be wrong on that.
By ‘any other dynamics would work’ I meant that the dynamics I gave, the ‘random hopping’ you (misguidedly) took issue with, isn’t essential to demonstrating my point. All that’s needed is the euiprobability of microstates. If that’s given, any dynamics will lead to violations of the second law, whether you want to accept that or not.
How do you suppose that could possibly work? How does the molecule know not to drift over into the other half of the room, for fear of changing the macrostate?
All that’s happening is that there are a lot fewer ways to change to a lower entropy macrostate than to one with higher entropy. Hence, the latter sort of thing happens more often.
Has science proved the equiprobability of all possible microstates in a system? This isn’t a given at all, since it violates the second law. What reason do I have to think it is so?
I apologize in advance for my ignorance of modern physics, which I suspect factor into your answer. All I’ve got to go by is grade school physical science, the few books I have read on the subject, and the internet.
I can’t even pretend to explain the mechanisms of molecular physics. But I thought the kinetic theory was compatible with the laws of thermodynamics - if so, somehow the molecules of a system in equilibrium will have to cancel each other out.
It is valid that two systems are in mutual (thermal) equilibrium if there is no net flow of heat when they are in diathermal contact. However, imagine just one isolated system: if it is not in equilibrium, then you can imagine that under some extreme conditions it might not even have a well-defined temperature. On the other hand, once the system is in equilibrium all the “random movements” make no difference to the macrostate, assuming it is sufficiently “macro”.
If you are suggesting that certain transitions are allowed but others are not then it is important to note that that is not the case: these transitions are reversible microscopic fluctuations and each transition is as likely to occur as its converse. Again, nothing is defied: in the macroscopic limit these fluctuations will be too small to detect.
This isn’t really the sort of thing one can prove, but denying it would lead to violation of several key tenets of modern science. For instance, reversibility: for a molecule to enter a certain region, leading to a higher-entropy macrostate, reversibility holds that the opposite must also be possible, which it wouldn’t be, if for some reason the fact that the macrostate has a high entropy should prohibit this sort of development. Likewise, local causality: the options for a molecule in a sufficiently big macroscopic system would suddenly depend on the configuration of the system all the way over there, without any interaction between the parts.
Furthermore, it would introduce a sort of ‘downward causation’ incompatible with the fundamentally reductionistic nature of physics, i. e. with the idea that fixing the microscopic dynamics suffices to fix everything, because suddenly, the motion of molecules no longer depends on their interactions with their surroundings, but also, on whether they are considered to be part of a larger system in some macrostate. Whatever mathematics one uses to describe the motion of the molecules then would not only depend on their position and momenta, but also on the macrostate they’re part of, which really basically throws the whole edifice of classical physics as based on Hamiltonian mechanics overboard.
Finally, the assumption of equiprobability is in fact a key ingredient in deriving macroscopic thermodynamics from microscopic statistical physics, as carried out chiefly by Boltzmann in the 1870s (so not that terribly modern). The implication of the possibility of violations of the second law was realized pretty much immediately, leading Boltzmann to propose his idea that the universe could be a spontaneous low-entropy fluctuation (however, the possibility of Boltzmann brains seems to doom this scenario).
There’s just… something that I’m missing here. Maybe I’m still hung up on the “random hopping”. I’ll sleep on it and maybe it will make sense tomorrow.
I was just re-reading Cycles of Time by Roger Penrose and find his discussion on pages 39-43 pertinent to this thread — he even shows apparent counterexamples to the Second Law.
Now here’s something I don’t understand. If a molecule enters a thermodynamic system from without, thereby imparting kinetic energy upon the system, that system is beyond the scope of the second law of thermodynamics. The process of a molecule entering a system is not adiabatic and the system is not isolated. The ensuing temperature change would be reversible at the system level by simply ejecting an equivalent amount of kinetic energy back into the environment, possibly the same molecule with the same energy coming out the opposite side of the system.