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  • Thermodynamics and Statistical Mechanics - Chapter 4 – Probability and the General Formalism
    Thermodynamics and Statistical Mechanics, 2002
    Co-Authors: Phil Attard
    Abstract:

    This chapter explains how to obtain the probability distribution that corresponds to a reservoir. It is the Constrained Total Entropy whose exponential gives the probability distribution for parameters exchangeable with a reservoir. The Constrained thermodynamic potential is the negative of the reservoir temperature times the Constrained Total Entropy, and hence it appears like a Boltzmann factor in determining the probability distribution. If the state of an isolated subsystem can represent a state of equilibrium with a reservoir, then the Entropy of the isolated subsystem in that state must be a concave function of its arguments. Since a system can be considered a reservoir for its parts, in general the stable states of matter are characterized by concave Entropy. The chapter discusses probability distributions concepts related to isolated system, equilibrium, and Gaussian probability. It also discusses Constrained and equilibrium potentials. Basic concepts of concavity of the equilibrium free energy and partition function and specific reservoirs are presented.