WordNet

(sports) the ratio of successful performances to opportunities
achieve or reach on average; "He averaged a C"
a statistic describing the location of a distribution; "it set the norm for American homes" (同)norm
an intermediate scale value regarded as normal or usual; "he is about average in height"; "the snowfall this month is below average"
amount to or come to an average, without loss or gain; "The number of hours I work per work averages out to 40" (同)average out
compute the average of (同)average out
lacking exceptional quality or ability; "a novel of average merit"; "only a fair performance of the sonata"; "in fair health"; "the caliber of the students has gone from mediocre to above average"; "the performance was middling at best" (同)fair, mediocre, middling
around the middle of a scale of evaluation; "an orange of average size"; "intermediate capacity"; "medium bombers" (同)intermediate, medium
approximating the statistical norm or average or expected value; "the average income in New England is below that of the nation"; "of average height for his age"; "the mean annual rainfall" (同)mean
lacking special distinction, rank, or status; commonly encountered; "average people"; "the ordinary (or common) man in the street" (同)ordinary
a coordinated outfit (set of clothing)
a cast other than the principals (同)supporting players
an assemblage of parts or details (as in a work of art) considered as forming a whole (同)tout_ensemble
a group of musicians playing or singing together; "a string ensemble"

PrepTutorEJDIC

『平均』;並み,標準 / 平均値 / 『平均の』;並みの,標準の / 〈数〉'を'『平均する』 / 平均して…'を'する(受動態にできない) / 平均して…となる
(一体をなすものとしてとらえられた各部分の)総体;全体的効果 / (調和のとれた)婦人服の一そろい,アンサンブル / (小人数の)合奏団,合唱団,アンサンブル / 《集合的に》(劇などの)共演者

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/06/08 02:12:48」(JST)

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In statistical mechanics, the ensemble average is defined as the mean of a quantity that is a function of the microstate of a system (the ensemble of possible states), according to the distribution of the system on its micro-states in this ensemble.

Since the ensemble average is dependent on the ensemble chosen, its mathematical expression varies from ensemble to ensemble. However, the mean obtained for a given physical quantity doesn't depend on the ensemble chosen at the thermodynamic limit. Grand canonical ensemble is an example of open system.

Canonical ensemble average

Classical statistical mechanics

For a classical system in thermal equilibrium with its environment, the ensemble average takes the form of an integral over the phase space of the system:

{\bar {A}}={\frac {\int {Ae^{-\beta H(q_{1},q_{2},...q_{M},p_{1},p_{2},...p_{N})}d\tau }}{\int {e^{-\beta H(q_{1},q_{2},...q_{M},p_{1},p_{2},...p_{N})}d\tau }}}

where:

is the ensemble average of the system property A,

is

, known as thermodynamic beta,

H is the Hamiltonian of the classical system in terms of the set of coordinates

and their conjugate generalized momenta

, and

is the volume element of the classical phase space of interest.

The denominator in this expression is known as the partition function, and is denoted by the letter Z.

Quantum statistical mechanics

For a quantum system in thermal equilibrium with its environment, the weighted average takes the form of a sum over quantum energy states, rather than a continuous integral:

Characterization of the classical limit

Ensemble average in other ensembles

The generalized version of the partition function provides the complete framework for working with ensemble averages in thermodynamics, information theory, statistical mechanics and quantum mechanics.

Microcanonical ensemble

It represents an isolated system in which energy (E), volume (V) and the number of particles (N) are all constant.

Canonical ensemble

It represents a closed system which can exchange energy (E) with its surroundings (usually a heat bath), but the volume (V) and the number of particles (N) are all constant.

Grand canonical ensemble

It represents an open system which can exchange energy (E) as well as particles with its surroundings but the volume (V) is kept constant.

This physics-related article is a stub. You can help Wikipedia by expanding it.

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English Journal

Electrophysiological effect and the gating mechanism of astragaloside IV on l-type Ca(2+) channels of guinea-pig ventricular myocytes.

Zhao M1, Shao D2, Yu L2, Sun X2, Wang Y2, Hu H2, Feng R2, Gao Q2, Guo F2, Hao L3.
European journal of pharmacology.Eur J Pharmacol.2015 Aug 5;760:27-35. doi: 10.1016/j.ejphar.2015.03.082. Epub 2015 Apr 16.
Astragaloside IV (AS-IV) is one of the main active ingredients of Astragalus membranaceus. This study is aimed to investigate AS-IV׳s effects on Ca(2+) channel activity of single cardiomyocytes and single Ca(2+) channels. Whole-cell Ca(2+) currents in freshly dissociated cardiomyocytes were measure
PMID 25891370

BCRP and P-gp relay overexpression in triple negative basal-like breast cancer cell line: a prospective role in resistance to Olaparib.

Dufour R1, Daumar P2, Mounetou E3, Aubel C4, Kwiatkowski F5, Abrial C5, Vatoux C2, Penault-Llorca F5, Bamdad M2.
Scientific reports.Sci Rep.2015 Aug 3;5:12670. doi: 10.1038/srep12670.
The triple negative basal-like (TNBL) breast carcinoma is an aggressive and unfavorable prognosis disease. Inhibitors of poly(ADP-ribose) polymerase such as Olaparib could represent a promising targeted therapy but their sensitivity against Multidrug Resistance proteins (MDR), which causes resistanc
PMID 26234720

On est ensemble: social capital and maternal health care use in rural Cameroon.

McTavish S1, Moore S2.
Globalization and health.Global Health.2015 Aug 1;11(1):33.
BACKGROUND: Every day approximately 1500 women worldwide die due to pregnancy or childbirth related complications. Maternal health care use is critical in reducing maternal mortality worldwide. Cameroon has one of the highest maternal mortality rates worldwide, but there is little knowledge about ma
PMID 26231180

Japanese Journal

Typicality and statewise entropy for classical field systems

Yoshida Kyo
EPL 110(6), 60001, 2015-06
… Typicality for the system is shown in the sense that, for functions of state which satisfy certain conditions including the invariance under the spatial translations of the state, the values of the functions at almost all individual states in a microcanonical ensemble are almost equal to their microcanonical ensemble averages. …
NAID 120005652086

Real time detection of farm-level swine mycobacteriosis outbreak using time series modeling of the number of condemned intestines in abattoirs

ADACHI Yasumoto,MAKITA Kohei
Journal of Veterinary Medical Science 77(9), 1129-1136, 2015
… For the modeling, at first, periodicities were checked using Fast Fourier Transformation, and the ensemble average profiles for weekly periodicities were calculated. … An Auto-Regressive Integrated Moving Average (ARIMA) model was fitted to the residual of the ensemble average on the basis of minimum Akaike's information criterion (AIC). …
NAID 130005100722

Effects of water vapor dilution on trace gas flux, and practical correction methods

HARAZONO Yoshinobu,IWATA Hiroki,SAKABE Ayaka,UEYAMA Masahito,TAKAHASHI Kenshi,NAGANO Hirohiko,NAKAI Taro,KOSUGI Yoshiko
農業気象 71(2), 65-76, 2015
… Water vapor dilution correction for ensemble-averaged data (SA-method) is also applicable, though not recommended in case of long-term average data for accurate flux determination, especially for data obtained at irregular source strength plots. … The application of the correction for water vapor dilution to previous tower-based flux data (measured over a wet sedge tundra in Barrow throughout the month of August, 2000) also resulted in an increase in source (positive) flux of 6.6% on average. …
NAID 130005075874