E-folding

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "E-folding" – news · newspapers · books · scholar · JSTOR (December 2023) (Learn how and when to remove this message)

In science, e-folding is the time interval in which an exponentially growing quantity increases by a factor of e;^[1] it is the base-e analog of doubling time. This term is often used in many areas of science, such as in atmospheric chemistry, medicine and theoretical physics, especially when cosmic inflation is investigated. Physicists and chemists 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, ΔX_i, will have decreased to ΔX_i /e where the number e ≈ 2.71828.

${\displaystyle T_{e}={\frac {T_{d}}{\ln(2)}}={\frac {t}{\ln({N(t)}/{N(0)})}}={\frac {t}{\ln(1+r/100)}}}$

• T_e e-folding time
• N(t) amount at time t
• N(0) initial amount
• T_d doubling time
• ln(2) ≈ 0.693 natural logarithm of 2
• r% growth rate in time t