A neuron perceives electrical signals like an ultrasensitive microphone picking up the faintest vibrations. Its "hearing apparatus" consists of ion channels — protein pores in the cell membrane that open in response to changes in transmembrane voltage generated by the movement of charged particles. However, this ion flow inevitably carries noise that limits the precision of information processing. The first to appear is shot noise — discrete fluctuations caused by each ion crossing the channel independently, delivering a microscopic electrical "punch," much like individual raindrops drumming randomly on a tin roof. For a single ion channel, this noise sets a limit on voltage detection accuracy at about 10 millivolts.

When the signal is instead produced by the collective action of hundreds of channels, shot fluctuations average out statistically, and another fundamental source of uncertainty comes to the fore — thermal noise, also known as Johnson–Nyquist noise. This is the incessant chaotic motion of molecules driven by thermal energy; in electrical circuits, it manifests as random voltage fluctuations across the membrane's resistance. Thermal noise is fundamentally unavoidable because it arises from the very temperature of the environment, and it sets the absolute lower threshold for neuron sensitivity.

Remarkably, the transition from shot-noise dominance to thermal-noise dominance occurs precisely at the ion channel densities found in real neurons. For instance, in the axon hillock, a specialized region of the neuron where action potentials are generated and speed and precision of signal transmission are critical, channel density is hundreds of times higher than in the cell body. This suggests that during evolution, the nervous system achieved an optimal compromise: it uses just enough molecular resources to operate near the physical limits imposed by the laws of thermodynamics and statistical physics, without wasting energy on excessive precision.