Entropy (order and disorder)
This stems from Rudolf Clausius' 1862 assertion that any thermodynamic process always "admits to being reduced [reduction] to the alteration in some way or another of the arrangement of the constituent parts of the working body" and that internal work associated with these alterations is quantified energetically by a measure of "entropy" change, according to the following differential expression:[1] where Q = motional energy ("heat") that is transferred reversibly to the system from the surroundings and T = the absolute temperature at which the transfer occurs.
In the years to follow, Ludwig Boltzmann translated these 'alterations of arrangement' into a probabilistic view of order and disorder in gas-phase molecular systems.
Similarly, in 1859, after reading a paper on the diffusion of molecules by Clausius, Scottish physicist James Clerk Maxwell formulated the Maxwell distribution of molecular velocities, which gave the proportion of molecules having a certain velocity in a specific range.
[2] In 1864, Ludwig Boltzmann, a young student in Vienna, came across Maxwell's paper and was so inspired by it that he spent much of his long and distinguished life developing the subject further.
[8] Technically, entropy, from this perspective, is defined as a thermodynamic property which serves as a measure of how close a system is to equilibrium—that is, to perfect internal disorder.
[9] Likewise, the value of the entropy of a distribution of atoms and molecules in a thermodynamic system is a measure of the disorder in the arrangements of its particles.
[11] Moreover, according to theoretical ecologist and chemical engineer Robert Ulanowicz, "that entropy might provide a quantification of the heretofore subjective notion of disorder has spawned innumerable scientific and philosophical narratives.
[11] The mathematical basis with respect to the association entropy has with order and disorder began, essentially, with the famous Boltzmann formula,
Unlike temperature, the putative entropy of a living system would drastically change if the organism were thermodynamically isolated.
Moreover, according to the third law of thermodynamics, at absolute zero temperature, crystalline structures are approximated to have perfect "order" and zero entropy.
[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 thermal motion, whenever heat is added to a working substance, the rest position of molecules will be pushed apart, the body will expand, and this will create more molar-disordered distributions and arrangements of molecules.
However, in common speech, order is used to describe organization, structural regularity, or form, like that found in a crystal compared with a gas.
Under suitable thermodynamic conditions, entropy has been predicted or discovered to induce systems to form ordered liquid-crystals, crystals, and quasicrystals.
[24] Yet, according to the second law of thermodynamics, because no heat can enter or leave the container, due to its adiabatic insulation, the system should exhibit no change in entropy, i.e. ΔS = 0.
Shannon's use of the term 'entropy' in information theory refers to the most compressed, or least dispersed, amount of code needed to encompass the content of a signal.
