E-folding
Encyclopedia
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
.
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
, e-folding is the time interval in which an exponentially growing
Exponential growth
Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...
quantity increases by a factor of e
E (mathematical constant)
The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
. This term is often used in theoretical physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, especially when cosmic inflation
Cosmic inflation
In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 1078 in volume, driven by a negative-pressure vacuum energy density. The inflationary epoch comprises the first part...
is investigated. Physicists often talk about the e-folding time scale that is determined by the proper time
Proper time
In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. The proper time depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a smaller elapsed time between two...
in which the length of a patch of space
Space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...
or spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
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
E (mathematical constant)
The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
.