Abstract
The idea that entropy is associated with the “arrow of time” has its roots in Clausius’s statement on the Second Law: “Entropy of the Universe always increases.” However, the explicit association of the entropy with time’s arrow arises from Eddington. In this article, we start with a brief review of the idea that the “increase in entropy” is somehow associated with the direction in which time increases. Then, we examine three different, but equivalent definitions of entropy. We find that none of these definitions indicate any hint of a relationship between entropy and time. We can, therefore, conclude that entropy is a timeless quantity. We also discuss the reasons as to why some scientists went astray in associating entropy with time’s arrow. Finally, we shall discuss Boltzmann’s H-Theorem, which is viewed by many as a proof of the Second Law of Thermodynamics.
Highlights
We believe that once the system attains an equilibrium, the −H (t) attains its maximum value, i.e., we identify the maximum over all possible distributions with the maximum of s measure of information (SMI) in the limit t → ∞: Entropy = lim [−H (t)] = Max SMI
When we remove a constraint, the state of the system changes with high probability to a new equilibrium state
When we remove a constraint, the entropy of the system changes with high probability towards a maximum
Summary
Open any book which deals with a “theory of time,” “time’s beginning,” and “time’s ending,”. You are likely to find the association of entropy and the Second Law of Thermodynamics with time [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. Unlike Boltzmann’s definition the SMI definition does not rely on calculations of the number of accessible states of the system It provides directly the entropy function of an ideal gas, and by extension, the entropy function for a system of interacting particles. The independence of entropy on time is most clearly revealed from the SMI-based definition of entropy. At this point it is appropriate to quote Einstein on Thermodynamics:. The cause for this association of entropy with time is that thermodynamics was used not “within the framework of its applicability”
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