9 Introduction to Entropy

Brokk Toggerson

Learning Objectives

By the end of this chapter, you should be able to…

  • Define entropy in terms of the number of microstates.
  • State the fundamental principle of statistical mechanics: that all microstates are equally likely.
  • Calculate the entropy for simple configurations.
  • From the entropy, determine the number of microstates available.

Key Terms

Macrostate – A “overall” picture of a system. This can be defined however the observer wishes. It could include such overall properties as volume, temperature, density, total energy, or more “contrived” properties such as the number of 1’s that result from rolling a handful of dice.

Microstate – The specific condition of each individual element of the system. If these are individual atoms, then we might speak of their positions, velocities, or other properties. In the case of multiple dice, we might speak of the result of each individual dice thrown.

– All microstates in a given macrostate are equally likely.

– A measurement of the total number of microstates for a given macrostate.


This concept is best described in video form. I have included a good video below.



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