Many microscopic processes require a system to cross an energy barrier before an event can occur. Thermal fluctuations make barrier crossing possible, producing thermally activated behavior.

A common empirical form is the Arrhenius relation

$$k=k_0\exp!\left(-\frac{Q}{RT}\right),$$

where $k$ is a rate-like coefficient, $k_0$ is a prefactor, $Q$ is an activation energy per mole, $R$ is the universal gas constant and $T$ is absolute temperature.

Taking logarithms gives

$$\ln k=\ln k_0-\frac{Q}{R}\frac1T.$$

Therefore an Arrhenius plot of $\ln k$ against $1/T$ is approximately linear when one activation mechanism dominates. Its slope is

$$-\frac{Q}{R}.$$

Why temperature matters so strongly

Because temperature appears in an exponential, a modest change in $T$ can change a rate by orders of magnitude. This is why diffusion, creep, chemical reactions and microstructural transformations can be almost frozen at one temperature and rapid at another.

An Arrhenius fit is not automatically a fundamental law. The prefactor and apparent activation energy can change if the dominant mechanism changes, and curvature in an Arrhenius plot can signal that one constant-$Q$ description is inadequate.

The general lesson is that barrier-controlled processes carry an exponential temperature sensitivity; each physical application determines what the coefficient $k$, barrier $Q$ and prefactor mean.