thermal noise

Every resistor, even one just sitting on the bench doing nothing, quietly makes its own faint hiss of voltage. The reason is heat: temperature is really just jiggling, and the electrons inside any resistor are forever in random thermal motion, like dust motes dancing in a sunbeam. Their ceaseless jostling produces a tiny, random, ever-present voltage at the resistor's terminals. This is thermal noise (also called Johnson noise), and it sets the quietest floor any circuit can ever reach.

The noise voltage is Vnoise(rms) = sqrt(4 times k times T times R times B), where k is Boltzmann's constant (1.38 x 10^-23 joules per kelvin), T is the absolute temperature in kelvin, R is the resistance, and B is the bandwidth in hertz over which you measure. Notice what that means: noise grows with the square root of resistance, of temperature, and of bandwidth, so halving the bandwidth only cuts the noise by sqrt(2), not by 2. Put in numbers: a 10 kilohm resistor at room temperature (300 K) over a 20 kHz audio bandwidth gives about sqrt(4 times 1.38e-23 times 300 times 10000 times 20000) which is roughly 1.8 microvolts rms. A 1 megohm resistor over a 1 MHz bandwidth gives about 128 microvolts.

Thermal noise is white, meaning it carries equal energy at every frequency, and you cannot filter it away without also narrowing the band your signal lives in. It is why high-impedance, wide-bandwidth, hot circuits are noisy, and why sensitive front ends use low source resistance, modest bandwidth, and sometimes outright cooling. Be honest about it: you cannot beat thermal noise with neater wiring or a cleaner layout, because it is set by physics. The best you can do is keep R, T, and B no larger than your signal genuinely needs.