Abstract

Although the Gamma distribution is known within statistical mechanics to describe the probability that a classical ideal gas at a fixed temperature occupies a given energy state it appears to have been all but forgotten. In this paper we present a new and much simpler derivation starting from the Maxwellian velocity distribution. The analysis is extended to open systems in which the number of particles fluctuates. Computer simulations using a hard‐sphere model of a classical ideal gas are used to support the theoretical considerations and show how the Gamma distribution applies in practice. The resulting probability distributions are used to calculate the Shannon information entropy which is then compared with the thermodynamic entropy. We point out an important proof in information entropy that also appears to have been overlooked in statistical thermodynamics and argue on the basis of the work presented here that information theoretic entropy and thermodynamic entropy, whilst obviously related, are not necessarily identical.