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  • Print publication year: 2015
  • Online publication date: April 2015

4 - Entropy and how the macroscopic world works


Microstate probabilities

In Chapter 3 we discussed the way the world works at a microscopic level: the interactions and laws governing the time evolution of atoms and molecules. We found that an important, unifying perspective for both quantum and classical descriptions is the concept of energy. Now we take a macroscopic point of view. What happens when many (~1023) molecules come together, when we cannot hope to measure individual atomic properties but can probe only bulk material ones? As the title of this chapter suggests, the relevant concept at the macro-resolution is entropy.

Remember that from a macroscopic perspective, we care about macrostates, that is, states of a system characterized by a few macroscopic variables, like E, V, N, T, or P. Empirical measurements generally establish values for properties that are the net result of many atomic interactions averaged over time, and we are thus able to describe a system only in terms of these large-scale, reduced-information metrics that smooth over the molecular world. The statement that a system is at one specific macrostate actually implies that it is evolving through a particular ensemble of many microscopic configurations.

We will focus on classical isolated systems because these offer the simplest introductory perspective. Let us imagine that a closed, insulated container of molecules evolves in time.

Further Reading
Callen, H., Thermodynamics and an Introduction to Thermostatistics, 3rd edn. New York: Wiley (1985).
Denbigh, K., The Principles of Chemical Equilibrium, 4th edn. New York: Cambridge University Press (1981).
Hill, T. L., An Introduction to Statistical Thermodynamics. Reading, MA: Addison-Wesley (1960); New York: Dover (1986).
Jackson, E. A., Equilibrium Statistical Mechanics. Mineola, NY: Dover (1968).
Khinchin, A. I., Mathematical Foundations of Statistical Mechanics. New York: Dover (1949).
Landau, L. D. and Lifshitz, E. M., Statistical Physics, 3rd edn. Oxford: Butterworth-Heinemann (1980).
McQuarrie, D. A., Statistical Mechanics. Sausalito, CA: University Science Books (2000).
Tester, J. W. and Modell, M., Thermodynamics and Its Applications, 3rd edn. Upper Saddle River, NJ: Prentice Hall (1997).
Tolman, R. C., The Principles of Statistical Mechanics. New York: Dover (1979).