On Quantum Entropy

Round 1

Reviewer 1 Report

Standard i.e. von Neumann entropy of quantum states is the founction of the state operator and can be used for example to discriminate between pure and mixed states. In the paper, the authors propose to consider another entropy - type quantity defined in terms of probability distributions of canonically conjugate observables (such as position and momentum). In thos case the natural definition can be formulated for pure states and such entropy quantifies the randomness of pure states ( in contrast to von Neumann  entropy). In the context of quantum field theory, such defined entropy is a relativistic scalar, is invariant under canonical transformations and under CPT transformation.

The paper contains an interesting discussion of non - standard notion of quantum entropy and is well prepared. In my opinion, this manuscript is worth to publish and can be accepted for publication in the journal Entropy.

Reviewer 2 Report

The present authors propose capturing information of a quantum state on the basis of the degrees offreedom of the state together with the always present intrinsic randomness.

 They introduce two new information quantifiers to such an effect.  They are a pair of conjugate observables that satisfy the uncertainty principle.
 One of them is a coordinate-entropy that possesses desirable properties, like invariance under canonical transformations, or Lorentz trasnformations, or CPT transformations.  They extend such entropy to mixed states as well.

The authors analyze the entropy evolution through the partition of quantum curves and prove that the Dirac’s Hamiltonian disperses information due to its positive Hessian, causing coherent states time evolution to increase entropy.

They also show that the entropy increases when an electron in an excited state of the hydrogen atom falls to the ground state emitting a photon and analyze
 collisions of two particles, each evolving as a coherent state.

The paper is interesting and well written. I recommend acceptance.

Comments for author File: Comments.pdf