I had discussion on statistical mechanics with my friend last night. I come to know, The relationship between entropy and disorder is studied in a discipline called statistical mechanics.

I have no cleare Idea about , How is Entropy Related to Disorder?

Can anyone help me to clear my mind.?

It is good to see you coming back to discuss your topic; connecting entropy and order/disorder can be paradoxical and often leads to surprising or even inappropriate conclusions.

As noted here modern science is therefoe veering away from offering this connection.

https://en.wikipedia...r_and_disorder)

This Wikipedia summary is a fair summary, and says nothing actually incorrect unlike many offerings, although it raises some questions it does not properly answer.

The connection really hinges on what you mean by order or disorder.

The definition of entropy is pretty well specified, swansont has provided a statistical definition, and has bender a physical one.

However there is no such convenient definition of either order or disorder. What is meant depends in part on the parameters of interest.

You have not discussed these further or indicated you mathematical level but you can't fully consider the question without some mathematics.

Going with the statistical approach, since it is in the title, here is a simple introduction.

Consider a chessboard : It has 64 squares.

Which means there are 64 ways to place a single black pawn on the (otherwise empty) board.

There is no reason to assume any of these positions or arrangements is 'better' than any other so we choose one square and call it 'order'.

If we place the pawn there the arrangement is 'ordered'.

If we place it anywhere else the arrangement is 'disordered'.

There is thus 1 possible arrangement called order but there are 63 possible ways of disorder.

Now we consider a **change** of arrangement.

If we make a single change to arrangement, i.e. move a disordered pawn to any other square, there are 62 ways of doing this whilst maintaining the disorder and only one way to change to an ordered pawn.

For this system a change is 62 times more likely to result in disorder than order.

This is only for one single pawn.

Now take all 8 black pawns and consider arrangements of them on the board.

You can place the first pawn in one of 64 ways i.e.on any square.

You can place the second pawn in one of 63 ways i.e.on any remaining square.

You can place the third pawn in one of 62 ways i.e.on any remaining square.

and so on.

In total this means there are 64 x 63 x 62 x 61 x 60 x 59 x 58 x 57 = 178462987637760 different arrangements.

So what is order now?

Is it perhaps some relationship between the positions of the pawns, say they are all in a straight line?

Well there are 2 ways this can be done if they are to remain on the same colour and another 16 ways if the colour does not matter.

This simple model can be developed to embody all the important characteristics of Statistical Mechanics which are, in relation to the OP.

1) The pawns are not distinguished. Every pawn is equivalent to every other, so any pawn in the order position constitutes order.

2) The arrangements are not distinguished so any position can be chosen as order.

3) It is changes to the position that offer meaningful properties.

4) When talking about the change, only the beginning and end positions are meaningful. No meaning is attached to the positions during the change.

Notes what I have called arrangements or positions are called states in Thermodynamics and Statistical Mechanics.

**Edited by studiot, 20 February 2017 - 02:39 PM.**