How is mechanics statistical? Do we basically find the probability of a ball rolling when we hit it?
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Statistichal mechanics is not the usual mechanics: it studies large numbers of particles that cannot possibly be studied individually.
With such a great number of particles though, you don’t care about the behaviour of a single one, but just about cumulative properties, that can be studied through statistics and probability theory.
Statistical mechanics are used to define bulk properties when something is comprised of many small elements – too many elements to realistically calculate independently, but when you consider the thing in application it effectively acts as a continuum.
It is usually used in the context of gasses/liquids.
Gasses are made of a great number of independent molecules, with different velocities and spins – but in most applications you can treat a gas as a continuous entity not made of discrete particles. Since it’s not really feasible to analyse a gas as trillions of separate particles you might assign a probability distribution to the gas defining what proportion of its particles have different velocities. Although straying into chemistry – you might be trying to assess how quickly a gas would cause something to corrode, which requires an interaction between a “fast” gas particle (that has enough energy to trigger the reaction) and a “hot” atom on the surface that’s corroding. If you know what fraction of atoms in the gas and on the surface have different energy levels, you can work out the rate at which interactions with sufficient energy for a chemical reaction occur.
TLDR: Things like gasses are made of lots of small particles, you can treat them like a continuous thing based on the statistics of the velocities of the particles.
Real ELI5
If you roll a painted ball down a hill it’s pretty easy know where it will leave a trail.
If you roll 500 balls that bump and knock into each other as they bounce down a slope it is much harder to know where each will roll.
If we don’t care exactly where it is painted on the hill, we can use statistical mechanics to get a good guess about how much and where the hill will be painted.
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