Fluctuations and the second law of thermodynamics

Summary

The problem of energy fluctuation of a small group of molecules in a physically incompressible system in thermal equilibrium is considered from the point of view of the dynamical evolution of the system. Through an appropriate solution of the time-dependent Liouville equation, it is shown that the system temperature is a constant of the motion, and that the phase density is canonical in form, involving a time-dependent Hamiltonian. It is concluded that in such a system the second law of thermodynamics is not violated contrary to current ideas. A comparison is made between the dynamical theory presented with traditional fluctuation theory based on stationary ensembles.