Observational entropy papers

Shows that classical maximal coarse-grained entropy (without the volume term that makes it different from OE), consistent with observed observable averages on each macrostate, converges to the microcanonical entropy in the long time limit. Results not directly inlcuding OE, but possibly could be modified and the results generalized to include OE.

Shows that OE generically increases in isolated systems based on statistical arguments: if the size of the smallest macrostate scales linearly with the size of the system, and evolution results in Haar measure random unitary, then the probability that OE will not be maximal is exponentially suppressed. More precise statemenent is given by introducing "asymptotic coarseness" of measurement, which guarantess that OE will be maximal as the dimension increases. Finally, the assumption of Haar random is weakened to 2-design.

Studies the Boltzmann entropy in the expansion of 200 classical hard disks when the partition is removed. Since OE is the sum of Shannon and Boltzmann entropies, and Shannon entropy is negligible in this case, it is almost the same as OE. Similar to the classical model simulated in Physical Review E 102 (3), 032106 (2020).

OE induces a partial ordering of coarse-grainings that differs from stochastic ordering.

Standard OE can be written as a quantum relative entropy with a maximally mixed state as a quantum prior. Three definitions for OE with general quantum priors are introduced, and their properties are discussed. Additionally, OE, and its generalizations, are interpreted as classical relative entropy between probabilities of forward and reversed processes.

Shows that OE is a continuous function of the state (by a direct inequality), and also of the coarse-graining (for a fixed state, and without a direct inequality).

Some relations between OE and other measures derived, for small dimensional systems.

OE measures the amount of extracted work from a source of states about which nothing is known, apart from what can be learned from a single type of coarse-grained measurement.

Proving identities between OE differences and the classical relative entropy. Showing that OE upper bounds the quantum relative entropy between the true and the recovered (coarse-grained) state of the system. Showing convexity properties of OE.

Defines entropy of an effect, which can be seen as the surprisal multiplied by the probability of an outcome. You can see this as a part of OE, which when summed gives the actual OE. Derives theorems about entropy of the sum of effects. Derives convexity properties, similar to those derived in "Observational entropy, coarse quantum states, and Petz recovery..."

Derives that starting in a product state and a product coarse-graining, where the coarse-graining is time-dependent and observable A stops commuting with observable on B as time goes on (non-conjugate observables), the change in OE is positive.

It is shown from very basic principles when observational entropy increases monotonically (although this is only a corollary in the paper).

Derived several inequalities between OE and functions derived from Rényi entropies.

Points out as a remark that observational entropy (called coarse-grained entropy in this case) of a black hole is upper-bounded by the Bekenstein-Hawking entropy. See Eq. (22). 

Discusses observational entropy (called coarse-grained entropy in this case), in relation to Hawking radiation, Eq. (4.2).

Book integrating OE in the concept of entropy production for open quantum systems.

Summary and overview of recent results for OE in isolated quantum systems, its interpretation and non-equilibrium thermodynamic entropy.

Application of OE to open quantum systems and derivation of a hierarchy of second laws. Based on a microscopic definition of temperature valid out of equilibrium, the conventional Clausius inequality emerges as a part of that hierarchy.

Short overview of OE.

Showing that the probability of the Universe collapsing into a small box is 50%. This collapse corresponds to a sharp decrease in OE.

OE can also be defined for classical systems, where phase-space density takes the role of the density matrix. Also, equivalent thermodynamic properties hold.

Popular science book, where OE is argued as the entropy that we have in mind when we say "Entropy of the Universe increases."

The first paper introducing the term "observational entropy." It revived the research on OE after Alfred Wehrl in the 70s.  Plenty of definitions and theorems, and applications of OE in thermodynamics. The first definition of OE that includes multiple projective coarse-grainings.

Showing that the classical master equation leads to the increase in OE.

Book in which von Neumann introduced OE for general projective coarse-grainings.