Entropy: A Physical Entity or a Mathematical Construct?

The notion of entropy is already more than 150 years old. During all this time, there have been many different interpretations and re-definitions of the concept. Even today, there is not a clear consensus about entropy and the enunciation of the Second Law of Thermodynamics. Several different reviews have been published, describing not only the history of entropy, but also the wide variety of opinions and criticisms that have emerged. We wanted to summarize some of the most important contributions to the development of the present understanding of entropy. We also wanted to indicate that all definitions of entropy are equally valid, considering that they are just mathematical definitions. It is not possible to validate or reject the existence of any definition of entropy. This also raises serious questions regarding the true physical existence of entropy. Were entropy a physical entity, it would probably be a reincarnation of the old "caloric". Even if entropy did not have a tangible physical counterpart, this concept remains useful for many different areas of science and engineering; of course, which particular definition of entropy is used should be clearly stated.