Friday, February 6, 2015

statistical mechanics - Does entropy really always increase (or stay the same)?



enter image description here


Consider this image. If the big (grey) molecules were all to spontaneously move to the left, and the small ones were to move to the right, there would be an increase in order.


While unlikely, wouldn't this mean that entropy decreases?



Answer



Your example is an example of a microstate in your sample, which is a statistical ensemble and its entropy is defined by the number of microstates possible.


enter image description here


Where S is the entropy and K is the Boltzman constant and Ω is the total number of microstates. One of these microstates you show contributes to the Ω as one state. It will immediately flow into another one as the kinematics unfreeze from your frozen picture.



So, no it is not an example of an entropy decrease.


To decrease entropy in an open system is possible. Consider crystals drawn out of a liquid phase. There is energy given up and the crystal appears ordered from disorder. The entropy of liquid+ crystal , in a closed system, increases. Live organisms continually decrease the entropy of their system, using chemical properties to release energy to the environment and increase the total entropy.


No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...