di P.M. Boria 

Part 1 (of 4): Entropy

1.1     ENTROPY

To understand the meaning of Entropy[1], the first pillar of this paper, it would be useful to start with its generalized, qualitative definition: it is an indicator of the state of disorder of a defined group of bodies.The greater is the disorder, the greater the Entropy (“Entropy; synonymous with disorder”: Helmholtz, 1821-1894).

We will proceed backwards until its first inception; a strictly thermodynamic origin.

To provide clarity, let us consider the following situation: a room containing a table and on the table a bottle which is sealed and filled with smoke (of unknown nature). An observer can take a photograph, as a witness, of the initial state of order: clearly defined are the bottle, the table, the smoke, which occupies a well defined volume, as well as the room (which constitutes our “universe”): system being observed plus environment.

Figure 1.1 – From the point of view of Thermodynamics, the only possible spontaneous transformation is that of increasing entropy.

Opening the bottle, Figure 1.1, will result in diffusion of the smoke into the room. After a certain period of time (let’s say a day) the observer will be able to record a state of increased disorder: the smoke has come out of the bottle.

One could imagine that after a million days the table could have disintegrated, or in any case, the interaction of this universe with others (caused, for example, by a cataclysm) would have resulted in the destruction of the table and the bottle, and finally of the room itself: the observer will take a different photograph. 

Since the observations could be thought to extend over an unlimited time, the photographs, in succession, will indicate an increasing state of disorder, in other words entropy. Adopting the language of Prigogine: the transformation towards increasing entropy “produced” positive entropy (the difference in entropy between the final and initial states ≥ 0), while those of decreasing entropy produce negative entropy.

In parentheses we note that the inverse transformation (the smoke re-entering into the bottle) could not occur due to at least two reasons, each sufficient in themselves: first, the escape of smoke is an asymptotic function and its concentration tends towards perfect uniformity in volume with infinite time; second, without a concentration gradient it is not possible to have any movement of mass within the expanded smoke.

Proceeding backwards in history we observe that the concept of entropy makes its first entry in physics thanks to the work of Clausius (Germany, 1822-1888), who was searching for principles of conservation which govern thermodynamics.

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