The fluctuation–dissipation theorem (FDT) is a fundamental principle in statistical mechanics that connects spontaneous fluctuations in a system at equilibrium to its response to external perturbations. In essence, it states that the way a system reacts to small disturbances is directly related to how it naturally fluctuates when undisturbed.
This relationship reveals that dissipation (how a system loses energy when pushed out of equilibrium) is governed by the same mechanisms that produce thermal noise and fluctuations at equilibrium.
Key Features:
- Applies to systems in thermal equilibrium.
- Provides a way to predict response functions (like conductivity, viscosity, or susceptibility) from measurements of equilibrium fluctuations.
- Bridges microscopic dynamics and macroscopic behavior.
Examples:
- In electrical circuits, Johnson–Nyquist noise (thermal voltage noise in resistors) is related to resistance (energy dissipation).
- In Brownian motion, the random motion of particles is connected to the viscous drag they experience when forced.
- In material science, mechanical or magnetic responses can be predicted using fluctuation data.
The fluctuation–dissipation theorem is a powerful tool for understanding how equilibrium properties determine dynamic behavior, with applications in physics, chemistry, biology, and even economics.