Boltzmann Entropy & Equilibrium in Non-Isolated Systems

Abstract

The microscopic approach of statistical mechanics has developed a series of formal expressions that, depending on the different features of the system and/or process involved, allow for calculating the value of entropy from the microscopic state of the system. This value is maximal when the particles attain the most probable distribution through space and the most equilibrated sharing of energy between them. At the macroscopic level, this means that the system is at equilibrium, a stable condition wherein no net statistical force emerges from the overall behaviour of the particles. If no force is available then no work can be done and the system is inert. This provides the bridge between the probabilistic equilibration that occurs at the microscopic level and the classical observation that, at a macroscopic level, a system is at equilibrium when no work can be done by it.

Keywords: Approximate equiprobability, Approximate isoenergeticity, Boltzmann entropy, Boltzmann factor, Canonical ensemble, Canonical partition function, Dominating configuration, Energetic (im)probability, Equal probabilities, Equilibrium fluctuations, Fundamental thermodynamic potential, Gibbs free energy, Grand canonical ensemble, Helmholtz free energy, Maximization of entropy, Microcanonical partition function, Microcanonical system, Minimization of energy, Temperature, Thermostatic bath.