Statistical mechanics of colloids and Boltzmann’s definition of the entropy

  title={Statistical mechanics of colloids and Boltzmann’s definition of the entropy},
  author={Robert H. Swendsen},
  journal={American Journal of Physics},
  • R. Swendsen
  • Published 13 February 2006
  • Physics
  • American Journal of Physics
The Boltzmann entropy as traditionally presented in statistical mechanics textbooks is only a special case and not Boltzmann's fundamental definition. The difference becomes important when the traditional expression for the entropy is applied to colloids, for which it makes incorrect predictions. Boltzmann's original definition of the entropy in terms of the probabilities of states of composite systems leads to consistent and correct statistical mechanics and thermodynamics. 
The definition of the thermodynamic entropy in statistical mechanics
Abstract A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released,
Thermodynamics of the System of Distinguishable Particles
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of
Thermodynamics of the System of Distinguishable Particles
The issue of the thermodynamics of a system of distinguishable particles is discussed and a straightforward way to get the corrected Boltzmann counting is shown, which can be justified in classical statistical mechanics.
Negative temperatures and the definition of entropy
The concept of negative temperature has recently received renewed interest in the context of debates about the correct definition of the thermodynamic entropy in statistical mechanics. Several
Continuity of the entropy of macroscopic quantum systems.
  • R. Swendsen
  • Physics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2015
This paper analyzes and calculates the thermodynamic entropy for large but finite quantum mechanical systems and preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics.
Gibbs volume entropy is incorrect.
We show that the expression for the equilibrium thermodynamic entropy contains an integral over a surface in phase space, and in so doing, we confirm that negative temperature is a valid
Gibbs' Paradox and the Definition of Entropy
Gibbs’ Paradox is shown to arise from an incorrect traditional definition of the entropy that has unfortunately become entrenched in physics textbooks, which predicts a violation of the second law of thermodynamics when applied to colloids.
Footnotes to the history of statistical mechanics: In Boltzmann’s words
Although Ludwig Boltzmann was one of the primary founders of the field of statistical mechanics, very few contemporary physicists have actually read his papers. As a result, some of his ideas have
Choosing a Definition of Entropy that Works
Disagreements over the meaning of the thermodynamic entropy and how it should be defined in statistical mechanics have endured for well over a century. In an earlier paper, I showed that there were
Why colloidal systems can be described by statistical mechanics: some not very original comments on the Gibbs paradox
Colloidal particles are distinguishable. Moreover, their thermodynamic properties are extensive. Statistical mechanics predicts such behaviour if one accepts that the configurational integral of a


Fundamentals of Statistical and Thermal Physics
This book is designed for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum. The book is devoted to a discussion of some of the basic physical
Statistical Mechanics of Classical Systems with Distinguishable Particles
The properties of classical models of distinguishable particles are shown to be identical to those of a corresponding system of indistinguishable particles without the need for ad hoc corrections. An
The Gibbs Paradox
ABSTRACT The dependence of the entropy on the number of molecules can never be found from studying closed systems. The argument based on counting states of particles, indistinguishable or not, is