Open system trajectories specify fluctuating work but not heat.

@article{Talkner2016OpenST,
  title={Open system trajectories specify fluctuating work but not heat.},
  author={Peter Talkner and Peter H{\"a}nggi},
  journal={Physical review. E},
  year={2016},
  volume={94 2-1},
  pages={
          022143
        }
}
Based on the explicit knowledge of a Hamiltonian of mean force, the classical statistical mechanics and equilibrium thermodynamics of open systems in contact with a thermal environment at arbitrary interaction strength can be formulated. Yet, even though the Hamiltonian of mean force uniquely determines the equilibrium phase space probability density of a strongly coupled open system, the knowledge of this probability density alone is insufficient to determine the Hamiltonian of mean force… 

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