Next Article in Journal
Entropy Analysis of the Interaction between the Corner Separation and Wakes in a Compressor Cascade
Next Article in Special Issue
Non-Causal Computation
Previous Article in Journal
Invalid Microstate Densities for Model Systems Lead to Apparent Violation of Thermodynamic Law
Previous Article in Special Issue
CSL Collapse Model Mapped with the Spontaneous Radiation
Article Menu
Issue 7 (July) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(7), 322; https://doi.org/10.3390/e19070322

Entropic Phase Maps in Discrete Quantum Gravity

Department of Mathematics, William Carey University, 710 William Carey Parkway, Hattiesburg, MS 39401, USA
Received: 26 May 2017 / Revised: 20 June 2017 / Accepted: 25 June 2017 / Published: 30 June 2017
(This article belongs to the Special Issue Quantum Information and Foundations)

Abstract

Path summation offers a flexible general approach to quantum theory, including quantum gravity. In the latter setting, summation is performed over a space of evolutionary pathways in a history configuration space. Discrete causal histories called acyclic directed sets offer certain advantages over similar models appearing in the literature, such as causal sets. Path summation defined in terms of these histories enables derivation of discrete Schrödinger-type equations describing quantum spacetime dynamics for any suitable choice of algebraic quantities associated with each evolutionary pathway. These quantities, called phases, collectively define a phase map from the space of evolutionary pathways to a target object, such as the unit circle S 1 C , or an analogue such as S 3 or S 7 . This paper explores the problem of identifying suitable phase maps for discrete quantum gravity, focusing on a class of S 1 -valued maps defined in terms of “structural increments” of histories, called terminal states. Invariants such as state automorphism groups determine multiplicities of states, and induce families of natural entropy functions. A phase map defined in terms of such a function is called an entropic phase map. The associated dynamical law may be viewed as an abstract combination of Schrödinger’s equation and the second law of thermodynamics. View Full-Text
Keywords: quantum gravity; discrete spacetime; causal sets; path summation; entropic gravity quantum gravity; discrete spacetime; causal sets; path summation; entropic gravity
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Dribus, B.F. Entropic Phase Maps in Discrete Quantum Gravity. Entropy 2017, 19, 322.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top