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

Entropic Phase Maps in Discrete Quantum Gravity

Department of Mathematics, William Carey University, 710 William Carey Parkway, Hattiesburg, MS 39401, USA
Entropy 2017, 19(7), 322;
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)
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
Show Figures

Figure 1

MDPI and ACS Style

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

AMA Style

Dribus BF. Entropic Phase Maps in Discrete Quantum Gravity. Entropy. 2017; 19(7):322.

Chicago/Turabian Style

Dribus, Benjamin F. 2017. "Entropic Phase Maps in Discrete Quantum Gravity" Entropy 19, no. 7: 322.

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

Article Access Map by Country/Region

Back to TopTop