Where does concentration collide?

In chemistry, concentration is the amount of a dissolved substance present in a given amount of solution, most often expressed as amount concentration or molarity, the moles of solute per litre of solution. It is an intensive quantity: it does not depend on how much of the mixture you have, and it governs how fast reactions run and where chemical equilibria settle. The IUPAC Compendium of Chemical Terminology (the Gold Book), compiled by McNaught and Wilkinson in 1997, gives the standard definitions of concentration and its related quantities. The referent is a physical ratio of matter to volume in a beaker, not a market dominated by a few firms, a mind fixed on a task, or a random variable clustering near its average.[1]

Unit

One instance is a solute amount divided by solution volume, e.g. moles per litre

Recovery means

Not applicable

Measured by

Determined by titration, spectrophotometry, or other assays calibrated against known standards

In industrial economics, concentration measures how far a small number of firms account for most of the activity in a market, captured by tools such as the concentration ratio, the combined share of the largest few firms, or the Herfindahl-Hirschman index, the sum of squared market shares. Bain's 1951 study Relation of Profit Rate to Industry Concentration linked how concentrated an industry was to how profitable its firms were, helping found the structure, conduct, and performance tradition. Here concentration is a property of a whole industry, read from the distribution of sales across competitors, and it has nothing to do with molarity in a flask, focused attention in a person, or the spread of a random quantity.[2]

Unit

One instance is an index over an industry's firm shares, e.g. a concentration ratio or HHI

Recovery means

Not applicable

Measured by

Computed from firms' market shares in sales, output, or assets within a defined market

In psychology, concentration is holding attention steadily on one task or stream of information while resisting distraction. William James, in his 1890 The Principles of Psychology, described attention as the mind taking possession of one object out of several, its focalization and concentration of consciousness, and treated that narrowing as the core of an effortful mental state. The referent is a person's directed and sustained focus, felt, reportable, and measured by performance, not a ratio of matter in a solution, the grip of a few firms on a market, or the clustering of a random variable.[3]

Unit

One instance is a person's sustained focus on a single task over a stretch of time

Recovery means

Attention lapses and returns, and focus is restored by rest, motivation, or re-engaging the task

Measured by

Indexed by performance on sustained-attention and vigilance tasks, error and reaction-time lapses, and self-report

In probability and statistics, concentration describes how tightly a random variable stays near its expected value, so that large departures from the average become very unlikely. Concentration inequalities, such as Chebyshev's and Chernoff's bounds, put explicit limits on the probability of straying far from the mean, and the broader concentration of measure phenomenon says that a well-behaved function of many independent variables is almost constant. Boucheron, Lugosi, and Massart's 2013 book Concentration Inequalities gathers this theory into a single account. The referent is a mathematical statement about the spread of a random quantity, not a chemical ratio, a market's structure, or a person's focus.[4]

Unit

One instance is a bound on the probability that a random variable deviates from its mean

Recovery means

Not applicable

Measured by

Established by proof, using moment, variance, or exponential-moment arguments to bound tail probabilities