Symmetry and Entropy

Dear Colleagues,

The relation between symmetry and entropy is a deep one. For isolated systems that are meaningfully describable in terms of microstates and macrostates, entropy S obeys the second law of thermodynamics and never decreases as the system evolves. A macrostate of such a system possesses a natural symmetry, its invariance under permutations of the set of microstates corresponding to it. Macroevolution is generally convergent, with the same final macrostate resulting from (usually many) different initial macrostates. But microevolution is nonconvergent, where different microstates always evolve into different microstates. (Nonconvergence is related to time reversal symmetry.) With the degree of symmetry of a macrostate represented by the number of its corresponding microstates W (monotonically related to the order of the symmetry group W!), it follows from the Curie principle (or symmetry principle) that the degree of symmetry of a macrostate never decreases as the system evolves. This is the special symmetry evolution principle and it is isomorphic with the second law under interchange of S and W. These two quantities are indeed monotonically increasing functions of each other through the famous relation S = k log W. This special issue celebrates that relation.

Dr. Shu-Kun Lin
Managing Editor