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Roughly, the fluctuation theorem relates to the probability distribution of the time-averaged irreversible entropy production, denoted ¯.The theorem states that, in systems away from equilibrium over a finite time t, the ratio between the probability that ¯ takes on a value A and the probability that it takes the opposite value, −A, will be exponential in At.
All have the same trend, but more filtering leads to higher r 2 of fitted trend line. The least-squares fitting process produces a value, r-squared (r 2), which is 1 minus the ratio of the variance of the residuals to the variance of the dependent variable. It says what fraction of the variance of the data is explained by the fitted trend line.
For instance, transport coefficients [2] are closely related to time correlation functions through the Fourier transform; and the Green-Kubo relations, [3] used to calculate relaxation and dissipation processes in a system, are expressed in terms of equilibrium time correlation functions.
Time series: random data plus trend, with best-fit line and different applied filters. In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time.
So for an algorithm of time complexity 2 x, if a problem of size x = 10 requires 10 seconds to complete, and a problem of size x = 11 requires 20 seconds, then a problem of size x = 12 will require 40 seconds. This kind of algorithm typically becomes unusable at very small problem sizes, often between 30 and 100 items (most computer algorithms ...
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of ...
The trend does not have to be linear. Conversely, if the process requires differencing to be made stationary, then it is called difference stationary and possesses one or more unit roots. [2] [3] Those two concepts may sometimes be confused, but while they share many properties, they are different in many aspects. It is possible for a time ...
Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [l] is defined as the linear part of the change in the functional, and the second variation [m] is defined as the quadratic part. [22]