Discussion Overview
The discussion centers on the reconciliation of Boltzmann's H-theorem and the conservation of Gibbs entropy, exploring the definitions and implications of different entropy formulations in thermodynamics and statistical mechanics. Participants examine the behavior of entropy in systems not in thermodynamic equilibrium and the distinctions between fine-grained and coarse-grained Gibbs entropy.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant describes Boltzmann's H-theorem, stating that entropy grows until equilibrium is reached if a system is not in thermodynamic equilibrium.
- Another participant notes that Gibbs entropy, defined as the integral of W*logW over phase space, is a constant of motion, independent of thermodynamic equilibrium, as per the Liouville equation.
- A participant provides references for further reading on the differences between Gibbs and Boltzmann entropies, although they clarify that these references focus on equilibrium calculations, which do not directly address their question.
- One participant suggests that Gibbs entropy involves coarse graining over finite volumes of phase space, proposing that it is a sum rather than an integral.
- Another participant distinguishes between fine-grained and coarse-grained Gibbs entropy, asserting that fine-grained entropy is a constant of motion while coarse-grained entropy is not.
- A participant illustrates the relationship between fine-grained and coarse-grained volumes in phase space, explaining how the former remains constant while the latter increases, relating this to the concept of entropy.
Areas of Agreement / Disagreement
Participants express differing views on the implications of Gibbs entropy and its relationship to Boltzmann's H-theorem. There is no consensus on how these concepts reconcile, and multiple competing interpretations are present.
Contextual Notes
Participants note that the discussion involves assumptions about the definitions of entropy and the conditions under which they apply, particularly regarding equilibrium and the treatment of phase space.