thermal noise

Heat is just jiggling. In any resistor at room temperature the charge carriers are rattling around at random, kicked by thermal energy, and that endless microscopic stampede shows up at the terminals as a faint, restless voltage that never sits still. That hiss is thermal noise. You can't switch it off, you can't filter it away, and it doesn't care what your signal is doing — it's the static-on-a-radio floor that every analog circuit sits on top of. The hotter the part and the bigger the resistance, the louder the hiss, which is why low-noise front ends are often run cool and built from small resistances.

Here's the precise version once the intuition lands: a resistor R at absolute temperature T produces a flat, white noise voltage with power spectral density 4kTR (k is Boltzmann's constant, about 1.38e-23 J/K). "White" means equal power at every frequency, so the noise you actually see depends on how wide a bandwidth you let through: the RMS voltage over a band Δf is the square root of 4kTR·Δf. A 1 kΩ resistor, for instance, delivers roughly 4 nV per root-hertz at room temperature — open up a megahertz of bandwidth and that's already a few microvolts of irreducible fuzz.

This floor is what sets the smallest signal you can ever recover. Below it, your signal is simply buried in the hiss, and no amount of clever gain helps — amplify the signal and you amplify the noise right along with it. So the whole game in low-noise design is to keep the wanted signal comfortably above 4kTR: spend more current (higher gm), use only the bandwidth you truly need, lower the source resistance, and cool the part when you can. Thermal noise is the tax physics charges for working at a finite temperature, and you pay it in every analog signal path.