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
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
, or an analogue such as
. This paper explores the problem of identifying suitable phase maps for discrete quantum gravity, focusing on a class of
-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.
This is an open access article distributed under the Creative Commons Attribution License
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MDPI and ACS Style
Dribus, B.F. Entropic Phase Maps in Discrete Quantum Gravity. Entropy 2017, 19, 322.
Dribus BF. Entropic Phase Maps in Discrete Quantum Gravity. Entropy. 2017; 19(7):322.
Dribus, Benjamin F. 2017. "Entropic Phase Maps in Discrete Quantum Gravity." Entropy 19, no. 7: 322.
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