Quantum entropic ambiguities: Ethylene

A. P. Balachandran, Amilcar Queiroz, and S. Vaidya
Phys. Rev. D 88, 025001 – Published 1 July 2013

Abstract

In a quantum system, there may be many density matrices associated with a state on an algebra of observables. For each density matrix, one can compute its entropy. These are, in general, different. Therefore, one reaches the remarkable possibility that there may be many entropies for a given state [R. Sorkin (private communication)]. This ambiguity in entropy can often be traced to a gauge symmetry emergent from the nontrivial topological character of the configuration space of the underlying system. It can also happen in finite-dimensional matrix models. In the present work, we discuss this entropy ambiguity and its consequences for an ethylene molecule. This is a very simple and well-known system, where these notions can be put to tests. Of particular interest in this discussion is the fact that the change of the density matrix with the corresponding entropy increase drives the system towards the maximally disordered state with maximum entropy, where Boltzman’s formula applies. Besides its intrinsic conceptual interest, the simplicity of this model can serve as an introduction to a similar discussion of systems such as colored monopoles and the breaking of color symmetry.

  • Received 7 May 2013

DOI:https://doi.org/10.1103/PhysRevD.88.025001

© 2013 American Physical Society

Authors & Affiliations

A. P. Balachandran1,2,*, Amilcar Queiroz3,†, and S. Vaidya4,‡

  • 1Department of Physics, Syracuse University, Syracuse, New York 13244-1130, USA
  • 2Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
  • 3Instituto de Fisica, Universidade de Brasilia, Caixa Postal 04455, 70919-970 Brasilia, DF, Brazil
  • 4Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012, India

  • *balachandran38@gmail.com
  • amilcarq@unb.br
  • vaidya@cts.iisc.ernet.in

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Issue

Vol. 88, Iss. 2 — 15 July 2013

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