Entropy Refers to Nothing in the Physical Reality

Pentcho Valev

"The definition of ΔS is strictly valid only for reversible processes, such as used in a Carnot engine. However, we can find ΔS precisely even for real, irreversible processes. The reason is that the entropy S of a system, like internal energy U, depends only on the state of the system and not how it reached that condition. Entropy is a property of state. Thus the change in entropy ΔS of a system between state 1 and state 2 is the same no matter how the change occurs. We just need to find or imagine a reversible process that takes us from state 1 to state 2 and calculate ΔS for that process. That will be the change in entropy for any process going from state 1 to state 2. (See Figure 2.)" https://pressbooks-dev.oer.hawaii.e...cs-disorder-and-the-unavailability-of-energy/

Figure 2:

Entropy is NOT a property of the state, but, for the sake of argument, let us assume that it is. The following fact is fatal for thermodynamics:

If there is an irreversible process between state 1 and state 2, there is no reversible process between state 1 and state 2. In other words, no irreversible process can be closed by a reversible process to become a cycle.

The problem is well known but, except for Jos Uffink, theoretical physicists never think of it:

Jos Uffink, professor at the University of Minnesota, p. 39: "A more important objection, it seems to me, is that Clausius bases his conclusion that the entropy increases in a nicht umkehrbar [irreversible] process on the assumption that such a process can be closed by an umkehrbar [reversible] process to become a cycle. This is essential for the definition of the entropy difference between the initial and final states. But the assumption is far from obvious for a system more complex than an ideal gas, or for states far from equilibrium, or for processes other than the simple exchange of heat and work. Thus, the generalisation to all transformations occurring in Nature is somewhat rash." http://philsci-archive.pitt.edu/313/

George Orwell: "Crimestop means the faculty of stopping short, as though by instinct, at the threshold of any dangerous thought. It includes the power of not grasping analogies, of failing to perceive logical errors, of misunderstanding the simplest arguments if they are inimical to Ingsoc, and of being bored or repelled by any train of thought which is capable of leading in a heretical direction. Crimestop, in short, means protective stupidity."

Uffink's text seems to imply that an irreversible process undergone by an ideal gas CAN be closed by a reversible process to become a cycle (e.g. irreversible isothermal expansion is followed by reversible isothermal compression). It can be shown that this is not a valid counterargument. The fatal fact remains universally true:

If there is an irreversible process between state 1 and state 2, there is no reversible process between state 1 and state 2.

How can a physicist oppose a concept that refers to nothing in the physical reality? Causa perduta. The physicist can only fall in deepest humiliation:

Arthur Eddington, Einstein's accomplice: "The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it to collapse in deepest humiliation." https://www.goodreads.com/quotes/947685-the-law-that-entropy-always-increases-holds-i-think-the

Pentcho Valev

Jos Uffink, Bluff your Way in the Second Law of Thermodynamics, p. 37: "THE ENTROPY PRINCIPLE (Clausius' version) For every nicht umkehrbar [irreversible] process in an adiabatically isolated system which begins and ends in an equilibrium state, the entropy of the final state is greater than or equal to that of the initial state. For every umkehrbar [reversible] process in an adiabatical system, the entropy of the final state is equal to that of the initial state." http://philsci-archive.pitt.edu/archive/00000313/

There is no such thing as "irreversible process in an adiabatically isolated system which begins and ends in an equilibrium state":

Uffink, p. 4: "The Second Law, in this view, refers to processes of an isolated system that begin and end in equilibrium states and says that the entropy of the final state is never less than that of the initial state (Sklar 1974, p. 381). The problem is here that, by definition, states of equilibrium remain unchanged in the course of time, unless the system is acted upon. Thus, an increase of entropy occurs only if the system is disturbed, i.e. when it is not isolated."

Clearly, the concept of entropy refers to things that happened in Clausius' head, a century and a half ago, and has nothing to do with the physical reality.

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