The generalized Boltzmann distribution is the only distribution in which the Gibbs-Shannon entropy equals the thermodynamic entropy.

@article{Gao2019TheGB,
  title={The generalized Boltzmann distribution is the only distribution in which the Gibbs-Shannon entropy equals the thermodynamic entropy.},
  author={Xiang Gao and E. Gallicchio and A. Roitberg},
  journal={The Journal of chemical physics},
  year={2019},
  volume={151 3},
  pages={
          034113
        }
}
We show that the generalized Boltzmann distribution is the only distribution for which the Gibbs-Shannon entropy equals the thermodynamic entropy. This result means that the thermodynamic entropy and the Gibbs-Shannon entropy are not generally equal, but rather the equality holds only in the special case where a system is in equilibrium with a reservoir. 

Topics from this paper

Shannon Entropy in Time-Varying Clique Networks
Shannon entropy in time-varying semantic networks of titles of scientific paper
Lattice–Gas–Automaton Modeling of Income Distribution
Molecules, Information and the Origin of Life: What Is Next?

References

SHOWING 1-10 OF 31 REFERENCES
Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences.
  • G. Crooks
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1999
The entropy concept for non-equilibrium states
  • E. Lieb, J. Yngvason
  • Mathematics, Physics
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2013
Thermodynamics and an Introduction to Thermostatistics
Microcanonical origin of the maximum entropy principle for open systems.
  • Julian Lee, S. Pressé
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
The heat and work of quantum thermodynamic processes with quantum coherence
Introduction To Modern Statistical Mechanics
Three detailed fluctuation theorems.
Thermodynamics from Information
...
1
2
3
4
...