So I just watched Kahn Academys video on Maxwells Demon and its quite obvious how he proves it in regards of how the demon will expend create more heat than will flow from the cooler to the hotter body. And I also assume that this question has been asked and probably debunked multiple times before but here goes:
If you remove the demon from the equation and just say that by chance all high energy particles in the cold body move to the hot body and vice versa.
Obviously thats quite unlikely but maybe not even that unlikely if you only look at the first few moments (say a couple of nanoseconds) after the two bodies are brought together.
So by that logic in the unlikely case that happens, within the system there is a net decrease in Entropy, right? Now on the scale of the universe that chance obviously gets much much smaller because it would need to happen on enough occasions within a timeframe for at least 10^80 particles, but still: there would be a chance that the second law does not hold.
Where am I wrong?
>>8207488
The second law of thermodynamics requires a system to be in thermodynamic equilibrium. Strictly, probably nothing in our world is ever in proper equilibrium. The example you mentioned (bringing two objects together and looking at t=x nanoseconds) is definitely not an equilibrium situation. Also the entropy increase in the second law, is also obviously referring to timescales in which a system reaches equilibrium..
>>8207507
So could I say that is the system is at two points in time at an equilibrium down to planck lenghts, which is even more unlikely but still not impossible, and between those two points my high energy particles travel to the hotter body and vice versa, that the law was violated?
This will obviously never happen on the scale of the universe and within the lifespan of the universe, but just as a thought experiment.
Or is the planck length completely meaningless in that regard and a system can actually never be at equilibrium because even sub planck lengths of difference would mean its not?
It's changed somewhat because of the accelerating expansion of the universe, but yes it is _"_"_possible_"_"_ for entropy to only decrease starting tomorrow
>>8207512
>at an equilibrium down to planck lenghts
I'm not sure if I understand you here. Equilibrium is, as all of thermodynamics, a macroscopic concept. Planck lengths are smaller then all objects we've ever used thermodynamics on.
So a the demon would use energy to keep track of the particles? This is the lamest proof I have ever seen.
>>8207535
In the original thought experiment a "demon" is operating a door which only lets through some particles. For that the demon would need to expend more heat that could flow between the objects. To be honest I dont get why this in particular was a big deal that apparently took decades to solve but maybe people were just stuck in their thinking like with monty hall...
>>8207523
Ok. I thought equilibrium was if the system was in a state where you could exactly determine the macroscopic properties because the systems particles added up to a specific temperature, pressure etc.
I guess Im wrong but what exactly does make a system in equilibrium (or in reality close to it) then?
The key terms here are possible and feasible. It is possible for all red to drift into B, but insanely unlikely, infeasible indeed. Even for very simple systems like this it works out you expect to wait longer than the heat death of the universe for it to happen by chance.
>>8207567
Uniform state (e.g. temp), no fluxes (e.g. no heat flux), some sort of time-independent behaviour, is what I would say.
>>8207600
Ok but if I say that the temperature and pressure are uniform with an exactness of less than one "planck-temperature" and "planck-pressure" (which I think you could derrive from the other planck units) then the flux would also be zero to that degree of exactness and equilibrium state would be there for a number of digits after zero that is supposedly enough to not have any physcial effect (as which the planck lengths are defined as far as Im aware).
Now say between this moment and another one similar to it there is the unlikely event of heat flowing from the cold to the hot body, then in that timeframe the entropy in the universe would decrease.
Im still convinced that there is a flaw here and its likely to do with planck units not actually being of matter here, but still I think its worth the thought.
>>8207586
Hasnt really anything to do with just how unlikely it is or how it definitely wont happen within the lifetime of the universe, IMO.
What matters is that if there is even the possibility of entropy decreasing, the second law is not actually entirely true, which, I dont know, may have other implications or might just be completely fine in the reality. But who cares about reality right?
Oh and while were on the topic of thermodynamics:
Can anyone real quick explain to me what the [math]n[\math] in the exponent there means.
I understand that when [math]n[\math] reaches [math]\kappa[\math] (the heat capacity ratio) the process becomes isentrope, and I know how to calculate [math]\kappa[\math].
>>8207633
fucked that one up royally...
This is the picrelated that I wanted I guess now I know for sure that its not backslash...
>>8207567
Its not even solved. Need morerigorous proof of demon spending more energy.
>>8207622
No equilibrium can appears only either before you open the gate, a long time after you open the gate or at all time if your transformation is adiabatic and reversible(or isentropic)
>>8207488
You can always calculate the probability that the entropy of the universe will decrease and it will always be greater than 0. That doesn't mean it'll ever happen. Some people think that makes the second law a weak statement. In reality though, it's a pretty strong statement that relies on statistics. I don't think your thinking is wrong--I think you may not like the theory.
>>8207698
I think the issue is that the 2nd law says "entropy always increases" whereas it should say "entropy tends to increase"
>>8207704
I've always seen the word "tends" or "tendency." I think the second law is one the most reliable and strong laws of physics. The third law is the one I get annoyed with. When stated correctly it looks so weird. If you say something like, "you can never get temperatures below 0 Kelvin," it sounds great, bit it isn't quite right. The statement about the specific heat of a perfect crystal going to 0 as temperature goes to 0 is so specific that it's weird to call it a law. All my opinion of course.
>>8207704
Who says that?
Neither Kelvin, Planck, or Classius say that.
>>8207698
Wait so its a somewhat popular idea that the second law isnt 100% correct?
I guess that makes sense really, since the entire field of thermodynamics is based on statistics.
Though I had already assumed that even if its not accurate, its accurate enough for literally any practical purpose. But sometimes it feels good to differentiate between 100% mathematically correct and almost 100% statistically correct...
>>8207718
Make mathematically sense, I think:
[math]C_{v,mol} = f / 2 * R[/math]
so if youre at zero degrees you have zero degrees of freedom and the equation becomes zero.
>>8207862
Right, but some systems have some entropy "frozen in," so it makes intuitive sense, but it isn't easy to show with rigor. You may sometimes hear people say something like, "physics tells us there is a nonzero probability that I could run at the wall and phase right through it." This is patently ridiculous because it will never happen. But yeah, it's statistical mechanics.
