# Ever increasing entropy

by mviswanathan
Tags: entropy, increasing entropy
 P: 36 I need some clarification on definition of Entropy. According to the simple example of the egg in the kitchen, the entropy of the whole egg is lower than that of a cracked egg. This, it is said due to the fact that, there are more ways to be broken than a whole egg. But, if one talks of a particular Macro state, it must refer to the macro state of the ‘particular cracked egg’ – the egg cracked exactly in a specific fashion. In such a case how can it be claimed that there are more micro-states corresponding to the cracked-egg than a whole egg. Or, one could be comparing a whole egg and ‘not-whole’ egg. Then, of course there are more ways of ‘not- whole’ egg than a whole egg. Then again, we can consider an egg ‘cracked-in- a-specific-fashion’ and the one ‘not-cracked-in- that-specific-fashion’. In this case there are more possibilities of the later than the former and the later could be a whole-egg. Does it mean that, in this case the whole-egg has more entropy than the cracked one? The same could also apply to the fallen down and broken pieces of a cup – broken and scattered in that particular fashion. Obviously, I am going wrong somewhere. Please help.
HW Helper
PF Gold
P: 2,532
Entropy is "not knowing." It's not correct to equate a general cracked egg with an egg that has a perfectly specified crack; their entropies are different.

I'm not accustomed to the egg analogy; I'm more used to thinking about it in terms of a deck of cards. A randomly shuffled deck has a higher entropy than an ordered deck, even through it's the same deck. You don't know the arrangement of cards. However, if you took a specific randomly shuffled deck and called its specific sequence the "mviswanathan sequence," then any deck with the mviswanathan sequence would have a low entropy--the same as an ordered deck--because you know the position of each card with no uncertainty.

This is why I disagree with the statement

 Quote by mviswanathan But, if one talks of a particular Macro state, it must refer to the macro state of the ‘particular cracked egg’ – the egg cracked exactly in a specific fashion.
because when you focus on an "egg cracked exactly in a specific fashion," you're not looking at the same system, but on a different, lower-entropy system. I hope that helps resolve the apparent contradiction.
 Sci Advisor P: 5,523 Mapes is correct- the broken egg/shuffled deck/broken cup has a high entropy because many microstates (the specific state of the brokeen egg/cup) correspond to the same macrostate- a state that is an average over certain thermodynamic variables. It's the same reason why a gas in a box, if specified to exist at a certain temperature T one macrostate), consists of an extremely large number of microstates- the specific positions and velocities of each molecule in the box.
 Sci Advisor P: 8,470 Ever increasing entropy It really depends on how you define "macro" vs. "micro" states. Different possible ways of cracking the egg are distinguishable on visual inspection at a macroscopic level, so I suppose you could define them all as different macrostates. The cracked egg vs. whole egg is really just meant as a conceptual analogy though, I don't think there's any "standard" way to define the macrostates for such a system, normally thermodynamics deals with more macroscopically uniform systems like gas-filled boxes where macrostates are defined in terms of the value of macro-parameters like temperature and pressure.
P: 36
 Quote by Mapes Entropy is "not knowing." ... because when you focus on an "egg cracked exactly in a specific fashion," you're not looking at the same system, but on a different, lower-entropy system. I hope that helps resolve the apparent contradiction.
I did not understand the first statement.

In the end, does it mean that there is no absolute value of entropy - and it depends on from where/what you are looking? Then how can one have a statement that the entropy of a closed system keeps going up?

May be it has to do with what a "system" means. Still on the egg-story - the whole egg and the broken egg with all the pieces, do they not refer to the same system since broken egg exactly has all the components of the original?

Or may be some difference, considering the binding forces/stresses in the original egg which got released (may be I am not using the right words) when the egg breaks?
HW Helper
PF Gold
P: 2,532
 Quote by mviswanathan In the end, does it mean that there is no absolute value of entropy - and it depends on from where/what you are looking? Then how can one have a statement that the entropy of a closed system keeps going up?
This is an excellent point. We do have an absolute value for entropy because of the conventions we adopt. The eggs, decks of cards, etc. are analogies, so let's go to the better example of a gas in a box that Andy brought up. Our convention is to measure the bulk temperature or total energy, which is relatively easy to do. (These are macrostate variables.) We cannot determine the momentum and position of each atom. But there are many possible values of momentum and position (i.e., possible microstates) that could produce a given temperature or total energy. We will never know which microstate we're in, and it changes every instant anyway. This is the "not knowing." We take the entropy to be proportional to the logarithm of the number of microstates, and we set a reference point of zero (or as close to zero as to be unmeasurable) at a temperature of absolute zero for a system in equilibrium. These conventions are what allow us to talk quantitatively about entropy and changes in entropy.