Entropy (order and disorder) Locally, the entropy can be lowered by external action. This applies to machines, such as a refrigerator, where the entropy in the cold chamber is being reduced, and to living organisms. This local decrease in entropy is, how- ever, only possible at the expense of an entropy increase in the surroundings. 1 History This “molecular ordering” entropy perspective traces its origins to molecular movement interpretations developed by Rudolf Clausius in the 1850s, particularly with his 1862 visual conception of molecular disgregation. Sim- ilarly, in 1859, after reading a paper on the diffusion of molecules by Clausius, Scottish physicist James Clerk Boltzmann’s molecules (1896) shown at a “rest position” in a solid Maxwell formulated the Maxwell distribution of molec- ular velocities, which gave the proportion of molecules having a certain velocity in a specific range. This was the In thermodynamics, entropy is commonly associated first-ever statistical law in physics.[3] with the amount of order, disorder, or chaos in a thermodynamic system. This stems from Rudolf Clau- In 1864, Ludwig Boltzmann, a young student in Vienna, sius' 1862 assertion that any thermodynamic process al- came across Maxwell’s paper and was so inspired by it ways “admits to being reduced to the alteration in some that he spent much of his long and distinguished life de- way or another of the arrangement of the constituent parts veloping the subject further. Later, Boltzmann, in efforts of the working body" and that internal work associated to develop a kinetic theory for the behavior of a gas, ap- with these alterations is quantified energetically by a mea- plied the laws of probability to Maxwell’s and Clausius’ sure of “entropy” change, according to the following dif- molecular interpretation of entropy so to begin to inter- ferential expression:[1] pret entropy in terms of order and disorder. Similarly, in 1882 Hermann von Helmholtz used the word “Unord- nung” (disorder) to describe entropy.[4] Z δQ ≥ 0 T 2 Overview In the years to follow, Ludwig Boltzmann translated these “alterations” into that of a probabilistic view of order and To highlight the fact that order and disorder are com- disorder in gas phase molecular systems. monly understood to be measured in terms of entropy, In recent years, in chemistry textbooks there has been a below are current science encyclopedia and science dic- shift away from using the terms “order” and “disorder” to tionary definitions of entropy: that of the concept of energy dispersion to describe en- tropy, among other theories. In the 2002 encyclopedia • A measure of the unavailability of a system’s energy Encarta, for example, entropy is defined as a thermody- to do work; also a measure of disorder; the higher namic property which serves as a measure of how close a the entropy the greater the disorder.[5] system is to equilibrium, as well as a measure of the dis- • A measure of disorder; the higher the entropy the order in the system. [2] In the context of entropy, "perfect greater the disorder.[6] internal disorder" is synonymous with “equilibrium”, but since that definition is so far different from the usual def- • In thermodynamics, a parameter representing the inition implied in normal speech, the use of the term in state of disorder of a system at the atomic, ionic, or science has caused a great deal of confusion and misun- molecular level; the greater the disorder the higher derstanding. the entropy.[7] 1 2 3 PHASE CHANGE • A measure of disorder in the universe or of the avail- tropy, then many are often puzzled as to the nature of ability of the energy in a system to do work.[8] the “ordering” process and operation of evolution in rela- tion to Clausius’ most famous version of the second law, Entropy and disorder also have associations with which states that the universe is headed towards maximal equilibrium.[9] Technically, entropy, from this perspec- “disorder”. In the recent 2003 book SYNC – the Emerg- tive, is defined as a thermodynamic property which serves ing Science of Spontaneous Order by Steven Strogatz, for as a measure of how close a system is to equilibrium — example, we find “Scientists have often been baffled by that is, to perfect internal disorder.[2] Likewise, the value the existence of spontaneous order in the universe. The of the entropy of a distribution of atoms and molecules laws of thermodynamics seem to dictate the opposite, in a thermodynamic system is a measure of the disor- that nature should inexorably degenerate toward a state der in the arrangements of its particles.[10] In a stretched of greater disorder, greater entropy. Yet all around us we out piece of rubber, for example, the arrangement of the see magnificent structures—galaxies, cells, ecosystems, molecules of its structure has an “ordered” distribution human beings—that have all somehow managed to as- [14] and has zero entropy, while the “disordered” kinky dis- semble themselves.” tribution of the atoms and molecules in the rubber in the The common argument used to explain this is that, lo- non-stretched state has positive entropy. Similarly, in a cally, entropy can be lowered by external action, e.g. so- gas, the order is perfect and the measure of entropy of lar heating action, and that this applies to machines, such the system has its lowest value when all the molecules are as a refrigerator, where the entropy in the cold cham- in one place, whereas when more points are occupied the ber is being reduced, to growing crystals, and to living gas is all the more disorderly and the measure of the en- organisms.[2] This local increase in order is, however, tropy of the system has its largest value.[10] only possible at the expense of an entropy increase in the [2][15] In systems ecology, as another example, the entropy of surroundings; here more disorder must be created. a collection of items comprising a system is defined as a The conditioner of this statement suffices that living sys- measure of their disorder or equivalently the relative like- tems are open systems in which both heat, mass, and or lihood of the instantaneous configuration of the items.[11] work may transfer into or out of the system. Unlike tem- Moreover, according to theoretical ecologist and chemi- perature, the putative entropy of a living system would cal engineer Robert Ulanowicz, “that entropy might pro- drastically change if the organism were thermodynami- vide a quantification of the heretofore subjective notion cally isolated. If an organism was in this type of “iso- of disorder has spawned innumerable scientific and philo- lated” situation, its entropy would increase markedly as sophical narratives.”[11][12] In particular, many biologists the once-living components of the organism decayed to [11] have taken to speaking in terms of the entropy of an or- an unrecognizable mass. ganism, or about its antonym negentropy, as a measure of the structural order within an organism.[11] The mathematical basis with respect to the association 3 Phase change entropy has with order and disorder began, essentially, with the famous Boltzmann formula, S = k ln W, which Owing to these early developments, the typical exam- relates entropy S to the number of possible states W in ple of entropy change ΔS is that associated with phase which a system can be found.[13] As an example, consider change. In solids, for example, which are typically or- a box that is divided into two sections. What is the prob- dered on the molecular scale, usually have smaller en- ability that a certain number, or all of the particles, will tropy than liquids, and liquids have smaller entropy than be found in one section versus the other when the par- gases and colder gases have smaller entropy than hotter ticles are randomly allocated to different places within gases. Moreover, according to the third law of thermo- the box? If you only have one particle, then that system dynamics, at absolute zero temperature, crystalline struc- of one particle can subsist in two states, one side of the tures are approximated to have perfect “order” and zero box versus the other. If you have more than one particle, entropy. This correlation occurs because the numbers of or define states as being further locational subdivisions different microscopic quantum energy states available to of the box, the entropy is lower because the number of an ordered system are usually much smaller than the num- states is greater. The relationship between entropy, or- ber of states available to a system that appears to be dis- der, and disorder in the Boltzmann equation is so clear ordered. among physicists that according to the views of thermo- From his famous 1896 Lectures on Gas Theory, Boltz- dynamic ecologists Sven Jorgensen and Yuri Svirezhev, mann diagrams the structure of a solid body, as shown “it is obvious that entropy is a measure of order or, most [13] above, by postulating that each molecule in the body has a likely, disorder in the system.” In this direction, the “rest position”. According to Boltzmann, if it approaches second law of thermodynamics, as famously enunciated a neighbor molecule it is repelled by it, but if it moves by Rudolf Clausius in 1865, states that: farther away there is an attraction. This, of course was a Thus, if entropy is associated with disorder and if the revolutionary perspective in its time; many, during these entropy of the universe is headed towards maximal en- years, did not believe in the existence of either atoms or 3 molecules (see: history of the molecule).[16] According to these early views, and others such as those developed by William Thomson, if energy in the form of heat is added to a solid, so to make it into a liquid or a gas, a common depiction is that the ordering of the atoms and molecules becomes more random and chaotic with an increase in temperature: Thus, according to Boltzmann, owing to increases in ther- mal motion, whenever heat is added to a working sub- stance, the rest position of molecules will be pushed apart, Entropy “order"/"disorder” considerations in the process of adiabatic demagnetization the body will expand, and this will create more molar- disordered distributions and arrangements of molecules.