The concept of entropy is fascinating.
It was born in the second half of the 19th century in a new scientific field, called thermodynamics, which aimed to describe changes in the form of another new physical quantity called energy. Entropy was introduced to account for some of their irreversible features.
Energy itself is a difficult concept that has no definition, except that given by a conservation principle (see R. Feynmann
). It is therefore not surprising that a notion derived from it is itself obscure. But there, the confusion is even greater, a threshold is crossed : entropy is in fact linked to a subjective and anthropocentric quantity, namely the quantity of information that we lack to completely represent the system under consideration.
This introduction of subjectivity into “hard sciences” is already amazing. Added to this is the fact that the concept of entropy is invoked in practically all scientific fields: from cosmology (“the entropy of the universe tends to a maximum”, R. Clausius
) to life science (“A living organism continually increases its entropy and thus tends to approach the dangerous state of maximum entropy, which is death”, E. Schrödinger
) passing by data compression and coding
and computer science
Recently, I put my two cents in this matter.
Landauer’s principle states that the logical irreversibility of an operation, such as erasing one bit, whatever its physical implementation, necessarily implies its thermodynamical irreversibility.
In this paper, a very simple counterexample of physical implementation (that uses a two-to-one relation between logic and thermodynamic states) is given that allows to erase one bit in a thermodynamical quasistatic manner (i.e. that may tend to be reversible if slowed down enough).
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In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling’s formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account. The use of the Stirling’s exact formula forces us to reintroduce them into the already proposed solutions of well-know puzzles such as the extensivity paradox or the Gibbs’ paradox of joining two volumes of identical gas.
Introducing the Boltzmann distribution very early in a statistical thermodynamics course (in the spirit of Feynmann) has many didactic advantages, in particular that of easily deriving the Gibbs entropy formula. In this note, a short derivation is proposed from the fundamental postulate of statistical mechanics and basics calculations accessible to undergraduate students.
Even today, the concept of entropy is perceived by many as quite obscure. The main difficulty is analyzed as being fundamentally due to the subjectivity and anthropocentrism of the concept that prevent us to have a sufficient distance to embrace it. However, it is pointed out that the lack of coherence of certain presentations or certain preconceived ideas do not help. They are of three kinds : 1. axiomatic thermodynamics; 2.