In science, e-folding is the time interval in which an exponentially growing quantity increases by a factor of e. This term is often used in theoretical physics, especially when cosmic inflation is investigated. Physicists often talk about the e-folding time scale that is determined by the proper time in which the length of a patch of space or spacetime increases by the factor e mentioned above.
In finance the logarithmic return or continuously compounded return, also known as force of interest, is the reciprocal of the e-folding time.
The term e-folding time is also sometimes used similarly in the case of exponential decay, to refer to the timescale for a quantity to decrease to 1/e of its previous value.
The process of evolving to equilibrium is often characterized by a time scale called the e-folding time, τ. This time is used for processes which evolve exponentially toward a final state (equilibrium). In other words if we examine an observable, X, associated with a system, (temperature or density for example) then after a time, τ, the initial difference between the initial value of the observable and the equilibrium value, ΔXi, will have decreased to ΔXi /e where the number e ~ 2.71828.