What Defines Order and Disorder in the Context of Entropy?

[Sidewalk]

Hi All -

OK, I understand that entropy increases over time, thermodynamic arrow , etc. But I don't fully grasp the concept in simple terms. I know that there are apparently many more states of disorder for a particular system than order (like Hawking says, puzzle pieces in a box). So if we shake the box randomly, then at a later time it is much more likely that the pieces will be in a state of "disorder" than order. Also, a cup on table which falls off, and becomes shards is then in a state of disorder and will never move itself back together to an ordered state. I also understand that if we glued it all back together we would be releasing energy and heat and therefore increasing the entropy of the universe over all, so I get the concept in principle.

My question is more about the definition of an ordered state. We view a cup on a table as being ordered, and pieces on a floor as being disordered, but a cup is one thing, and each piece on the floor is also one thing. Just because it is in pieces, aren't all those pieces beautifully ordered systems in their own right (even though WE didn't make them that way). What if I created a meticulously crafted piece of art which consisted of a bunch of perfectly placed cup shards on the floor. How is this more disordered than the cup on the table ? It just seems like we say it is disordered in pieces because we have decided what it should be like arbitrarily...
Why are pieces of a puzzle on a table which lie in a random pattern more "disordered" than when they are formed to make the picture of the puppy ?

I just need a little guidance...thanks for your help all..
Sidewalk

 

[Crosson]

First of all, I recommend learning about what entropy really is, because you have (clearly, by your question) reached the point of thinking beyond those "disorder" analogies.

In short, there are many more ways that the ceramic molecules could arrange themselves into shards on the floor then there are ways for them to arrange themselves as a cup.

Even though the entropy of the cup would be a computable number, and the entropy of the shards would be a computable number, any physicist who has better things to do would declare the shards to have a higher entropy without doing the calculation.

 

[Claude Bile]

The terms order and disorder are relative (like heavy and light). State A is more ordered than state B if there a less possible rearrangements for state A than state B.

Note that statistical thermodynamics doesn't say that a system is guaranteed to be more disordered over time, it just says that it is overwhelmingly probable.

Statistical Thermodynamics bases its definitions on a microscopic level, so trying to think of these concepts macroscopically invites confusion.

Claude.