How order and disorder defined for entropy?

[GME]

Entropy is the measure of ored and disorder. But who tells that what is order and what is disorder? Isnt it a relative or subjective thing? How to define it in general, or it can be definet only for thermodinamic systems?

 

[mikeph]

"order" is a subjective term which humans tend to associate with macroscopic states that correspond to relatively few microscopic states. To borrow a typical example, of all the possible ways of arranging grains of sand, very few lead to sandcastles, which we call "ordered". There are far more ways of arranging the grains which just lead to a pile of sand, which we call "disordered".

The entropy link arises from the disparity in the number of microstates which correspond to a given macrostate.

If we assume the temporal transition between microstates is random, and a disordered macrostate corresponds to more microstates than an ordered one, we're likely to observe a transition from order to disorder as time proceeds.

 

[Chestermiller]

I'd like to elaborate on what MickyW said. For an isolated system, the amount of disorder can by quantified by the number of linearly independent quantum mechanical microstates that the system can exhibit. The larger the number of (equally probable) quantum mechanical microstates, the more disorder. The entropy is proportional to the natural log of the number of quantum mechanical microstates. If you want to learn more about this, get a book on Statistical Thermodynamics, such as Hill's book.