Local Fluctuations and Local Observers in Equilibrium Statistical Mechanics

The distribution function associated with a classical gas at equilibrium is considered. We prove that apart from a factorisable multiplier, the distribution function is fully determined by the correlations among local momenta fluctuations. Using this result we discuss the conditions which enable idealised local observers, who are immersed in the gas and form a part of it, to determine the distribution ‘from within’. This analysis sheds light on two views on thermodynamic equilibrium, the ‘ergodic’ and the ‘thermodynamic limit’ schools, and the relations between them. It also provides an outline for a new definition of equilibrium that is weaker than full ergodicity. Finally, we briefly discuss the possibility that the distribution can be determined by external observers. r 2001 Elsevier Science Ltd. All rights reserved.