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 Emilio Gallicchio and Adrian E. 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. 
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References

SHOWING 1-10 OF 31 REFERENCES
Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences.
  • G. Crooks
  • Economics, Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1999
TLDR
A generalized version of the fluctuation theorem is derived for stochastic, microscopically reversible dynamics and this generalized theorem provides a succinct proof of the nonequilibrium work relation.
The entropy concept for non-equilibrium states
  • E. Lieb, J. Yngvason
  • Physics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2013
TLDR
The conclusion is that it is generally not possible to find a unique entropy that has all relevant physical properties, but it is shown that one can define two entropy functions, called S− and S+, which, taken together, delimit the range of adiabatic processes that can occur between non-equilibrium states.
Thermodynamics and an Introduction to Thermostatistics
GENERAL PRINCIPLES OF CLASSICAL THERMODYNAMICS. The Problem and the Postulates. The Conditions of Equilibrium. Some Formal Relationships, and Sample Systems. Reversible Processes and the Maximum Work
Entropy production along a stochastic trajectory and an integral fluctuation theorem.
TLDR
The integrated sum of both Delatas(tot) is shown to obey a fluctuation theorem (exp([-Deltas( tot) = 1 for arbitrary initial conditions and arbitrary time-dependent driving over a finite time interval)).
Microcanonical origin of the maximum entropy principle for open systems.
  • Julian Lee, S. Pressé
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
TLDR
It is shown that the target function for deriving the canonical distribution emerges as a natural consequence of partial maximization of the entropy over the bath degrees of freedom alone, and provides an alternative justification for the principle of path entropy maximization as well.
From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
Derivation of the canonical (or Boltzmann) distribution based only on quantum dynamics is discussed. Consider a closed system which consists of a mutually interacting subsystem and a heat bath, and
The heat and work of quantum thermodynamic processes with quantum coherence
Energy is often partitioned into heat and work by two independent paths corresponding to the change in the eigenenergies or the probability distributions of a quantum system. The discrepancies of the
Introduction To Modern Statistical Mechanics
Thermodynamics, fundamentals conditions for equilibrium and stability statistical mechanics non-interacting (ideal) systems statistical mechanical theory of phase transitions Monte Carlo method in
Three detailed fluctuation theorems.
TLDR
It is shown that each of them, the total, the adiabatic, and the nonadiabatic trajectory entropy, separately satisfies a detailed fluctuation theorem.
Negative entropy and information in quantum mechanics
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum
...
...