In complexity science, linear systems are systems that can be understood as a whole by understanding the individual parts. The opposites of linear systems are complex systems, which exhibit emergent macroscopic behaviors due to nonlinear dynamics between individual agents.
One example of linear interaction is temperature, which is an average over the activity of gas molecules. Here, the average is meaningful because of limited interaction between individual variables.
Linearity is axiomatically defined in § Linear Algebra via Vector spaces and ring modules: linear transformations respect addition and scaling.