- rate of change of a quantity across space or along a dimension
- mathematically: vector of partial derivatives pointing in the direction of steepest increase
- temperature gradients drive heat flow (Fourier’s law)
- concentration gradients drive diffusion (Fick’s law)
- pressure gradients drive fluid flow
- electrochemical gradients across cell membranes power ATP synthesis and nerve impulses
- altitude gradients shape climate zones, vegetation bands, and species distribution
- gradient descent: optimization algorithm that follows the negative gradient to minimize a loss function
- central to machine learning, thermodynamics, fluid dynamics, and ecology