I'm in high school and I was studying some topics related to heat transfer. While studying, I was curious about why heat strictly flowed from a higher temperature (more energy) to a lower temperature (less energy). I did some research and I came across ideas related to the second law of thermodynamics. I understand that the law is statistical in a truer sense. I'm curious about the size/ dimensions at the which the probability of the normal behaviour of the second law of thermodynamics decreases appreciably.
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$\begingroup$ There are some false assumptions in your question. Please read this Q and its answers and see if it addresses your question. physics.stackexchange.com/q/491179 $\endgroup$– g sCommented Jun 18 at 17:11
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$\begingroup$ See also the links in Does Fluctuation Theorem prove the 2nd Law of Thermodynamics?. $\endgroup$– ChemomechanicsCommented Jun 18 at 18:41
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3$\begingroup$ Voting to reopen. This is clear. Large collections of atoms can be well predicted by probability. Small collections have more variability. At what size does the variability get so big that we would likely not see the expected heat flow. $\endgroup$– mmesser314Commented Jun 18 at 20:55
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1$\begingroup$ I think there is a misconception about thermodynamics here. TD is a timeless theory. You are asking a question that is tied to an arbitrarily chosen time scale. If you make your measurement integration time longer, then smaller systems will behave as expected. If you make it infinitely short, then not even the largest systems will appear to be in equilibrium. $\endgroup$– FlatterMannCommented Jun 19 at 4:31
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(Not an expert)
In a statistical experiment the noise (i.e., the random fluctuations) is also known as Poisson noise, and it can be shown to be proportional to $1/ \sqrt{N}$, where $N$ is the number of events.
So it comes down to how precise you need your results to be. If you're conducting an experiment on $1 \rm{mol}$ of atoms, then your noise level is about $1.3 \times 10^{-12}$. In other words, you'll get about 12 digits of precision before random fluctuations start to be significant. If your experiment is not this precise, then other errors start to dominate well before the second law breaks down. The reverse applies if you only have a few hundred atoms.
Therefore, to answer your question, you need to first define what "decreases appreciably" means. How good is your experimental setup? How large are the other errors? ... etc.
