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Statistical analysis is the analysis of a very large number of particles / sample space where the general behaviour and trends of these particles is studied. But this also means that its probabilistic. That is, the properties of individual particles may and most definitely will deviate from the general trends. As in nuclear fission and calculation of their half lives. It doesn't seem to be possible to know whether a nucleus will split or not. And most of kinetic theory and thermodynamics seem to be statistics. The individual particles are way weirder.

So why, even though a lot of deviations from the general trend exist, statistical analysis is still used? Is it really impossible to analyze the individual particles?

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  • $\begingroup$ Yes - even if it were possible in principle (as it is in classical mechanics) how would you go about describing the motion of $6\times10^{23}$ particles in a mole of gas (even if you neglect internal motions, since each "particle" actually has structure)? $\endgroup$
    – NickD
    May 10 '19 at 15:16
  • $\begingroup$ @NickD Well, the computation powers of modern super computers have drastically improved. Is it still not enough to do such an analysis? $\endgroup$
    – evamPUNdit
    May 10 '19 at 15:18
  • $\begingroup$ @evamPUNdit : $10^{23}$ is a huge number. How would you even store the initial conditions of your system, let alone determine its evolution? $\endgroup$ May 10 '19 at 15:20
  • $\begingroup$ So it's a practical impossibly to do such a computation. $\endgroup$
    – evamPUNdit
    May 10 '19 at 15:22
  • $\begingroup$ It is indeed practically impossible. But even if it was doable, what would you do with answer? Extracting useful information from that amount of data is non-trivial. (unless you do the obvious thing at look at average values, but then what have you achieved that could not have been done with a statistical approach?) And then there is a similar problem with the inital conditions. How are you going to measure the initial positions of all those particles so you know how to start your simulation? $\endgroup$ May 10 '19 at 15:27
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I want to address this:

. As in nuclear fission and calculation of their half lives. It doesn't seem to be possible to know whether a nucleus will split or no

This is even worse than classical statistical mechanics which ends up in probabilities because of large numbers and the boundary conditions needed. Fission and all of nuclear physics are in the realm of quantum mechanics which is inherently probabilistic, even with one nucleus, and there is no way to even imagine overcoming this, at least in main stream theories.

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