Is Entropy Truly Subjective?

[DaveC426913]

So I get into these discussions on other ... less scientific ... fora, and then run into trouble and have to come here for correct answers.

I state these as assumptions but they are really questions. Please correct.

• Entropy is usually applied in a thermodynamics context, but it can be applied to any other source of order just as easily.
• A deck of cards can have its entropy measured.
• A fresh, sorted deck of cards has the lowest entropy possible, as it is in the highest ordered state possible.

But:

• The "order" of a deck of cards is entirely arbitrary. There's nothing objective about sequential human symbols.
• I could just as arbitrarily decide that the property of interest isn't sequential printed numbers, rather - I don't know - weight. The deck of cards is at its lowest entropic state when they are sorted heaviest card (most ink) to lightest card.
• I could even leave the property of interest the same and arbitrarily decide what is ordered and what is not:
  • I start with a sequential deck of cards. I decide they are ordered.
  • I shuffle them, and measure the disorder.
  • I then declare the new state to be perfectly ordered, and shuffle again.

So, either entropy is dependent on the property (or properties) of interest (and therefore subjective) or I am misapplying the concept of entropy.

 

[hilbert2]

Entropy isn't really a property of a single microstate, e.g. a way of ordering a deck of cards, or a combination of particle position and momenta in a classical point particle ideal gas. It's a property of a thermodynamical macrostate, like a combination of variables $P,V,n,T$ of an ideal gas, and it gets larger when there is a greater number of microstates that are consistent with that apparent macroscopic state.

It's a bit difficult to define "macroscopic" variables for a deck of cards, but you could for instance sum the number of red cards in the deck that have a black card both before and after them to obtain a variable that is some kind of average over the microstate variables.

 

[Lord Jestocost]

Shuffled Cards, Messy Desks, and Disorderly Dorm Rooms — Examples of Entropy Increase? Nonsense!
by F. L. Lambert
http://entropysite.oxy.edu/shuffled_cards.html#c1