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Residual entropy is the difference in entropy between a non-equilibrium state and crystal state of a substance close to absolute zero. This term is used in condensed matter physics to describe the entropy at zero kelvin of a glass or plastic crystal referred to the crystal state, whose entropy is zero according to the third law of thermodynamics .
This broader terminology is used when quantiles are used to parameterize continuous probability distributions. Moreover, some software programs (including Microsoft Excel) regard the minimum and maximum as the 0th and 100th percentile, respectively. However, this broader terminology is an extension beyond traditional statistics definitions.
Quantile functions are used in both statistical applications and Monte Carlo methods. The quantile function is one way of prescribing a probability distribution, and it is an alternative to the probability density function (pdf) or probability mass function, the cumulative distribution function (cdf) and the characteristic function.
The entropy of a closed system, determined relative to this zero point, is then the absolute entropy of that system. Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times the Boltzmann constant k B = 1.38 × 10 −23 J K −1.
The residual entropy of a fluid has some special significance. In 1976, Yasha Rosenfeld published a landmark paper, showing that the transport coefficients of pure liquids, when expressed as functions of the residual entropy, can be treated as monovariate functions, rather than as functions of two variables (i.e. temperature and pressure, or ...
The von Neumann entropy formula is an extension of the Gibbs entropy formula to the quantum mechanical case. It has been shown [ 1 ] that the Gibbs Entropy is equal to the classical "heat engine" entropy characterized by d S = δ Q T {\displaystyle dS={\frac {\delta Q}{T}}\!} , and the generalized Boltzmann distribution is a sufficient and ...
The studentized bootstrap, also called bootstrap-t, is computed analogously to the standard confidence interval, but replaces the quantiles from the normal or student approximation by the quantiles from the bootstrap distribution of the Student's t-test (see Davison and Hinkley 1997, equ. 5.7 p. 194 and Efron and Tibshirani 1993 equ 12.22, p. 160):
Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares estimates the conditional mean of the response variable across values of the predictor variables, quantile regression estimates the conditional median (or other quantiles ) of the response variable.