Thermodynamics as the continuum limit of statistical mechanics Available to Purchase

The thermodynamic limit in statistical mechanics is often equivalent to a properly defined continuum limit, in which Boltzmann’s constant k vanishes together with the microscopic scales of length and time. In this continuum limit, which is the missing link between statistical mechanics and the historical development of thermodynamics, all microscopic fluctuations are suppressed, just as the quantum mechanical uncertainties are in the classical limit; these two limits are similar, but can be taken independently. The continuum limit is to be preferred above the thermodynamic limit when macroscopic dependences on space or time are present and may help to solve conceptual problems. As an example, capillary phenomena are discussed with particular attention to Kelvin’s equation. The enforced behavior of coupling constants in the continuum limit stresses the phenomenological and approximate status of thermodynamics. The relation with other reduction schemes of macroscopic physics is indicated, and possible consequences for ergodic theory are sketched.