Demography and the canonical ensemble

The Gibbs canonical ensemble of statistical mechanics is used to describe the probability distribution of the age classes of mothers of new-borns in an age-structured population. The Malthusian parameter emerges as a Lagrange multiplier corresponding to a generation time constraint, while a new perturbation parameter appears as the Lagrange multiplier corresponding to a maternity constraint. Classical Lotka stability reduces to the unperturbed case of the more general canonical ensemble model. The model is used in a case study of the female (peninsular) Malaysian population of 1970. The Malthusian parameter and perturbation are calculated easily by linear regression. Use of the model identifies an anomaly in the population due to the effects of World War II.