What Are First and Second Order Changes?

[khil_phys]

Many a times, in papers written on experimental work, there are statements like "there are no first order changes in time, but only those of the second order". What do such statements mean?

 

[mathman]

In general terms, the order refers to the relationship between change in one variable to change in another. First order means the change in the second variable is proportional to change in the first. Second order means change in the second variable is proportional to the square of the change in the first. Since these terms are used in discussing small changes, a second order change is much smaller than a first order change.