April 2009 clip on the origin and meaning of the term entropy by American chemical engineer Libb Thims.

In thermodynamics, entropy, symbol S, as defined in 1862 by German physicist Rudolf Clausius, is the energy equivalence-value of the transformation of a working body of atoms or molecules during a change state due to the action of the passage of heat into or out of the body, across its boundary, quantified by the value:

where Q is an inexact differential quantity of heat at an absolute temperature T that is produced from work due to the forces exerted by the constituent molecules of the body in question upon each other. [1] In 1865, Clausius redefined the differential form of entropy dS as:

making the derivative of heat a complete differential or path independent state function, the logic of which became embodied in what Clausius defined as the "second main principle" of the mechanical theory of heat. The mathematical expression of entropy was conceived by Clausius to quantify the effect of irreversibility (or the irreversible change of state of a body), in the working body, e.g. a body of steam in a steam engine, during an engine cycle; an effect that French physicist Sadi Carnot assumed, in 1824, did not occur due to his view that heat was form of caloric particles.

Overview
In general, according to Clausius, when a body (working body) changes its state, work is performed externally and internally at the same time, the exterior work having reference to the forces which extraneous bodies exert upon the body under consideration, and the interior work to the forces exerted by the constituent molecules of the body in question upon each other. The interior work is for the most part so little known, and connected with another equally unknown quantity (in fact with the increase of heat actually present in the body) in such a way, that in treating of it we are obliged in some measure to trust to probabilities; whereas the exterior work is immediately accessible to the observation and measurement, and thus admits of more strict treatment.

A listing of [mostly incorrect] definitions of entropy in a letter to The Electrician (London) from Sydney Evershed, January 09, 1903, supposedly in connection to the great “what is entropy debate” (1902-1904) started by British electrical engineer James Swinburne. [4]

As such, to avoid everything hypothetical, we can exclude the interior work, by confining heat operations to the consideration of cyclical process— that is to say, operations in which the modifications that the body undergoes are so arranged that the body finally returns to its original condition. In such operations the interior work which is performed during the several modifications, partly in a positive sense and partly in a negative sense, neutralizes itself, so that nothing but exterior work remains, for which the theorem of the equivalence of transformations can then be demonstrated with mathematical strictness.

In addition, if the quantity of heat Q passes from a body whose temperature is T1 into another whose temperature is T2, the equivalence-value of this transformation is:

Where T is a function of the temperature which is independent of the kind of process by means of which the transformation is effected, and T1 and T2 denote the values of this function which correspond to the temperatures of bodies one and two. By separate considerations, according to Clausius, T is in all probability the absolute temperature. These two expressions further enable us to recognize the positive or negative sense of the transformations. In the first, Q is taken as positive when work is transformed into heat, and as negative when heat is transformed into work. In the second, we may always take Q as positive, since the opposite senses of the transformations are indicated by the possibility of the difference:

being either positive or negative. It will thus be seen that the passage of heat from a higher to a lower temperature is to be looked upon as a "positive transformation", and its passage form a lower to a higher temperature as a "negative transformation".

If we represent the transformations which occur in a cyclical process by these expressions, the relation existing between them can be stated in a simple and definite manner. If the cyclical process is reversible, the transformations which occur therein must be partly positive and partly negative, and the equivalence-values of the positive transformations must be together equal to those of the negative transformations, so that the algebraic sum of all the equivalence-values become = 0. If the cyclical process is not reversible, the equivalence values of the positive and negative transformations are not necessarily equal, but they can only differ in such a way that the positive transformations predominate.

The theorem respecting the equivalence-values of the transformations may accordingly be stated thus: The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing. The mathematical expression for this theorem is as follows. Let dQ be an element of the heat given up by the body to any reservoir of heat during its own changes, heat which it may absorb from a reservoir being here reckoned as negative, and T the absolute temperature of the body at the moment of giving up this heat, then the equation:

must be true for every reversible cyclical process, and the relation:

must hold good for every cyclical process which is in any way possible. The value of dQ/T is called entropy. [1]

Entropy of the universe tends to a maximum
American physicist Michael Guillen argues that the following formulation of the second law:

which states that the entropy of the final state of the universe will be greater than or ‘maximal’ as compared to the initial state entropy of the universe, is one the of the five equations that most changed the world; along with Isaac Newton’s law of universal gravitation, Daniel bernoulli’s law of hydrostatic pressure, Michael Faraday’s law of electromagnetic induction, and Albert Einstein’s mass-energy equivalence relation. [5]

Human system entropy
In human systems, the definition of entropy is the same with the translation that the "working body" is defined such that instead of water molecules, confined to the internal regions of a steam engine, put in alternating contact with a hot body (a fire) and a cold body (cool water), driven to do mechanical work (push a piston), we have human molecules, confined to the internal regions of various regions of social systems, put in alternating contact with a hot body (the day sun) and a cold body (the cool night sky), driven to do the daily work of life, e.g. economic work, social work, volunteer work, household work, parenting work, territorial expansion work, interpersonal work, relationship work, etc. [2]

From a reaction point of view, i.e. human chemistry point of view, boundaries to "working bodies" of human systems, i.e. interactive collections of human molecules confined to economic systems, are defined as being the the 90 percent probability regions in which a specific number of socially interactive or energetically-coupled humans are found. In this point of view, entropy is defined as the internal system energy (internal work) dissipated as humans act on each other, energy that does not find conversion into system external work.

Entropy of a human molecule
The concept of "human entropy" is the entropy value of individual person or human molecule or species of human molecules at a specific reference point in time. The first to make the suggestion that each person has a different value of entropy was American engineer William Fairburn in his 1914 book Human Chemistry.

In theory, each individual person can be assigned an entropy value, in reference to a base value, similar to smaller molecules. Shown below, for instance, are standard measures of entropy for four different molecules:


A table such as this is similar to the "material entropy" postulate, but with reference on the measure of entropy per species.

Origin of term

See main: Entropy (etymology)

Between 1850 and 1865, Clausius published a series of nine memoirs, which in 1865 were collected in the textbook Mechanical Theory of Heat. The outline of the theoretical development of the concept and terminology of entropy, went through a number of name changes: "an expression was needed" (1850), equivalence-value (1854), "equivalence-value of all uncompensated transformations" (1856), "disgregation" (1862), "transformation-content" and then finally arriving at the word entropy (1865). [3]

See also
● Entropy (quotes)

(b) Thims, Libb. (2007). Human Chemistry (Volume Two), (preview). Morrisville, NC: LuLu.
3. Clausius, R. (1865). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
4. Reeve, Sidney. (1907). “The Question of Entropy”, Harvard Engineering Journal (pgs. 138-54), Vol. 6.
5. Guillen, Michael. (1996). Five Equations that Changed the World: the Power and Poetry of Mathematics (ch. 4: An Unprofitable Experience: Rudolf Clausius and the Second Law of Thermodynamics, pgs. 165-214). Hyperion.

Further reading
● Fast, J.D. (1962). Entropy - the Significance of the Concept of Entropy and its Applications in Science in Technology. New York: McGraw-Hill Book Co. Inc. ● Arnheiim, Rudolf. (1974). Entropy and Art: an Essay on Disorder and Order. University of California Press.
● McIntyre, Vonda N. (1981). The Entropy Effect. Publisher: Star Trek.
● Brooks, Daniel R. and Wiley E.O. (1988). Evolution and Entropy (2nd ed.). Chicago: University of Chicago Press.
● Dugdale, J.S. (1998). Entropy and its Physical Meaning. London: Taylor and Francis.
● Greven, Andreas, Keller, Gerhard, and Warnecke, Gerald. (2003). Entropy (Princeton Series in Applied Mathematics). Princeton University Press.
● Ben-Naim, Arieh. (2007). Entropy Demystified - the Second Law Reduced to Plain Common Sense. London: World Scientific.

External links
● Entropy – Wikipedia.