= Statistical physics
{wiki}
<Statistical physics> explains collective behavior using <probability distributions> over microscopic possibilities. Its central surprise is that incomplete microscopic knowledge can still produce precise predictions for <internal energy>, <entropy> and <heat capacity>. The bridge is <statistical mechanics>: specify the available <microstates>, assign their <probabilities>, then compute the <expected values> of measured quantities.
A <two-level system> already displays the idea. Warming it makes its higher <energy> more likely; its <heat capacity> first rises, then falls as the two <probabilities> approach equality. With two distinguishable units, merely counting <microstates> explains why the middle <energy> has twice the <state degeneracy>. These small examples expose the machinery before the much larger sums needed for a <photon gas> or an <Ising model>.
The appeal is economical: the same microscopic <energies> and <probabilities> explain both an average reading and its <variance>. A measurement's spread therefore becomes useful physical information rather than an inconvenience to discard.
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