Fluctuations

Fluctuations are deviations of a quantity from its average value over time or space, arising from the inherent randomness of natural processes or from changing conditions. They are usually described by their amplitude, timescale, and statistical properties such as variance and noise type.

In physics, fluctuations are central to thermodynamics and quantum mechanics. Thermal fluctuations come from random molecular motion and lead to small, temporary deviations from equilibrium; quantum fluctuations persist even at very low temperatures in uncertain measurements. The fluctuation-dissipation theorem links spontaneous fluctuations to a system's response to external perturbations.

In statistics and data analysis, fluctuations refer to variability around a central tendency. They are quantified by variance or standard deviation and can be analyzed as time series using autocorrelation, power spectra, and other methods to identify trends, periodicities, or randomness.

In economics and finance, price fluctuations reflect changing supply and demand and market sentiment, yielding volatility. In climatology and ecology, fluctuations occur in temperature, precipitation, or population sizes, ranging from daily variability to long-term cycles such as El Niño or Milankovitch cycles. In biology, gene expression and physiological processes exhibit stochastic fluctuations that can influence cellular behavior.

Understanding fluctuations involves distinguishing intrinsic stochasticity from external influences, modeling with stochastic processes, and applying measurement techniques to extract meaningful signals. Fluctuation analysis informs about system dynamics, stability, and resilience.