{
  "id": "1904.03473",
  "version": "v1",
  "published": "2019-04-06T15:34:04.000Z",
  "updated": "2019-04-06T15:34:04.000Z",
  "title": "Entropy Non-Conservation and Boundary Conditions for Hamiltonian Dynamical Systems",
  "authors": [
    "Gerard McCaul",
    "Alexander Pechen",
    "Denys I. Bondar"
  ],
  "comment": "10 pages, 3 figures",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "physics.class-ph",
    "quant-ph"
  ],
  "abstract": "Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von-Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new dynamical phase associated with such a construction is identified. By choosing distributions not belonging to this class, we produce explicit examples of both free particle and harmonic systems evolving in a bounded phase-space in such a way that entropy is non-conserved. While these non-conserving states are classically forbidden, they may be interpreted as states of a quantum system tunnelling through a potential barrier boundary. In this case, the allowed boundary conditions are the only distinction between classical and quantum systems. We show that the boundary conditions for a tunnelling quantum system become the criteria for entropy preservation in the classical limit. These findings highlight how boundary effects drastically change the nature of a system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-06T15:34:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boundary conditions",
      "hamiltonian dynamical systems",
      "entropy non-conservation",
      "quantum system",
      "produce explicit examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}