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Entity

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Entity

Description

An elementary entity is a single countable object or single event. A number of defined elementary entities is a count. "An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles" (Bureau International des Poids et Mesures 2019).

If an object is defined as a group of particles, then the entity is the single group but not the particle. Entity X is the dimension X of the count NX. X and NX have the unit [x], and for X by definition x=1 (BEC 2020.1). For a count of x=1, the entity is refered to itself as a count.

Abbreviation: X [x]

Reference: BEC2020.1 doi10.26124bec2020-0001.v1

Communicated by Gnaiger Erich (2020-05-20) last update 2020-05-30

Entity and counting unit [x] as a self-referential unit

The big box is the system

The counting unit [x] is invariable one entity. Define one entity X=U [x] as a Unit-container U of fixed volume VNU [L·x-1] per Unit-containter full of particles E with fixed volume VNE [L·x-1] per particle E. Add a number NU [x] of Unit-containers U into a system (the big box) of volume V = VNU·NU [L]. The Unit-container carries an average number of particles E per Unit-container, NNE = NE·NU-1 [x·x-1=1]. The object (= entity 'Unit-container') of our study contains NE·NU-1 particles per Unit-container, whereas the system in which the objects with the particles E are enclosed contains NE = NU·NNE [x] particles.
  1. Note that the entity Unit-container U does not contain a number of entities NE of particles E. Only the system contains entities E, which are counted either as Unit-containers U or particles E.
  2. Note that the system does not contain NU·NE particles, which would have the dimension X2 [x2]. NE [x] is the number of particles contained in the system, whereas NNE [x·x-1=1] is the number of particles E per entity U.

The entity U is the system

Now we do not care about a big box, we focus strictly on the Unit-container as the system. This means, that the Unit-container U is not an entity X, since the system contains entities X. But if the Unit-container is defined as the system, then the systen cannot (or can?) contain itself: system =U. The system as defined contains a number NE of countable objects X, which are the particles E. Then X = E [x].

The particle E is the system

Now we do not care about a Unit-container, we focus strictly on the particle E as the system. This means, that the particle E is not an entity X, since the system contains X. The system contains itself. This self-referential condition is appreciated by the definition that the entity is refered to itself as a count for a count of x=1. This is appreciated further by considering the dimension X of the quantity 'count' at a level above all dimensions of physicochemical quantities.


Biological and chemical entities — and count

Countable biological objects are entities. An organism can be defined as an entity and counted, to obtain a count of organisms. This is simple for many but not all types of organisms. Think of counting humans or fish versus corals or multicellular algae. The single cell ce is the entity X=ce of the cell count NX=Nce. A cell count can be obtained for a suspension of cells using a cell counter. If the cell counter detects structurally defined elementary entities as cells, then a homogenate of the same cells does not contain a cell count, but it still contains the equivalent of a previously determined cell count. If the cell count was not determined before homogenization, alternative elementary entities may be defined to obtain a cell count, in which case a particular entity is the marker of a single cell. If the single cell of a particular cell type contains one nucleus, then the single nucleus is a marker of the cell. In principle, the same concept holds for molecules.
If a molecule is stable under a set of conditions, such as O2 or C6H12O6 at room temperature, then the pair of oxygen atoms or the atomic composition of glucose defines the entity 'oxygen molecule' or 'glucose molecule'. Typically we do not use an oxygen or glucose counter to measure the number of molecules, but charge or mass are markers of the number of molecules using electrochemical or gravimetric methods. The markers thus define the format and units of an entity, and the conversion between different formats is achieved by constants, such as the Avogadro constant, elementary charge, and Faraday constant.

Base quantities and count

SI-units-elementary quantities.png
Quantity Symbol for quantity Q Symbol for dimension Name of abstract unit uQ Symbol for unit uQ [*]
elementary entity *,$ UX U elementary unit x
count *,$ NX = N·UX X elementary unit x
amount of substance *,§ nX = NX·NA-1 N mole mol
charge *,€ Qel = zX·e·NX I·T coulomb C = A·s
length l L meter m
mass m M kilogram kg
time t T second s
electric current I I ampere A
thermodynamic temperature T Θ kelvin K
luminous intensity Iv J candela cd
[*] SI units, except for the canonical 'elementary unit' [x]. The following footnotes are canonical comments, related to iconic symbols.
* For the elementary quantities NX, nX, and Qel, the entity-type X of the elementary entity UX has to be specified in the text and indicated by a subscript: nO2; Nce; Qel.
$ Count NX equals the number of elementary entities UX. In the SI, the quantity 'count' is explicitly considered as an exception: "Each of the seven base quantities used in the SI is regarded as having its own dimension. .. All other quantities, with the exception of counts, are derived quantities" (Bureau International des Poids et Mesures 2019 The International System of Units (SI)). An elementary entity UX is a material unit, it is not a count (UX is not a number of UX). NX has the dimension X of a count and UX has the dimension U of an elementary entity; both quantities have the same abstract unit, the 'elementary unit' [x].
§ Amount nX is an elementary quantity, converting the elementary unit [x] into the SI base unit mole [mol] using the Avogadro constant NA.
Charge is a derived SI quantity. Charge is an elementary quantity, converting the elementary unit [x] into coulombs [C] using the elementary charge e, or converting moles [mol] into coulombs [C] using the Faraday constant F. zX is the charge number per elementary entity UX, which is a constant for any defined elementary entity UX. Qel = zX·F·nX

References

Bioblast linkReferenceYear
Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2. https://doi.org/10.26124/bec:2020-00022020
Gnaiger E (2021) The elementary unit — canonical reviewer's comments on: Bureau International des Poids et Mesures (2019) The International System of Units (SI) 9th ed. https://doi.org/10.26124/mitofit:200004.v22021
Gnaiger E et al ― MitoEAGLE Task Group (2020) Mitochondrial physiology. Bioenerg Commun 2020.1. https://doi.org/10.26124/bec:2020-0001.v12020


SI-units.png


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Entity, count, and number, and SI base quantities / SI base units
SI-units.png
Quantity name Symbol Unit name Symbol Comment
elementary UX elementary unit [x] UX, UB; [x] not in SI
count NX elementary unit [x] NX, NB; [x] not in SI
number N - dimensionless = NX·UX-1
amount of substance nB mole [mol] nX, nB
electric current I ampere [A] A = C·s-1
time t second [s]
length l meter [m] SI: metre
mass m kilogram [kg]
thermodynamic temperature T kelvin [K]
luminous intensity IV candela [cd]
Fundamental relationships
» Avogadro constant NA
» Boltzmann constant k
» elementary charge e
» Faraday constant F
» gas constant R
» electrochemical constant f
SI and related concepts
» International System of Units
» elementary unit x
» SI prefixes
» International Union of Pure and Applied Chemistry, IUPAC
» entity
» quantity
» dimension
» format
» motive unit
» iconic symbols



MitoPedia concepts: Ergodynamics