Entropy vs. reversibility

Statistical Mechanics (Spring, 2013)

May 15, 2013

Professor Susskind begins the lecture with 2 examples: (1) deriving the speed of sound in an ideal  gas; and (2) a single harmonic oscillator in a heat bath.  The harmonic oscillator example leads to a discrepancy with empirical observation that can only be resolved through quantum mechanics.  At low temperatures relative to the first excited state of the oscillator, quantum mechanics suppresses the energy of the harmonic oscillator.  Through this mechanism, certain modes of oscillation are "frozen out" until the system reaches higher temperatures.  Einstein proposed this quantized effect in 1907, which is one of the theories that led to the development of quantum mechanics.

Professor Susskind then discusses the apparent contradiction between the second law of thermodynamics, and the reversibility of classical mechanics.  If entropy always increases, reversibility is violated.  The resolution of this conflict lies in the (lack of) precision of our observations.  Undetectable differences in initial conditions lead to large changes in results.  This is the foundation of chaos theory.