Entropy for theories with indefinite causal structure

TL;DR

This paper introduces a new concept of entropy applicable to indefinite causal structures, combining quantum theory and general relativity, and proposes a measure of causal connectedness called the Q factor.

Contribution

It extends the causaloid framework to define a causally-unbiased entropy, providing a novel way to quantify causal connectedness in indefinite causal structures.

Findings

Defined causally-unbiased entropy within the causaloid framework

Introduced the Q factor as a measure of causal connectedness

Bridged concepts from quantum theory and general relativity

Abstract

Entropy is a concept that has traditionally been reliant on a definite notion of causality. However, without a definite notion of causality, the concept of entropy is not all lost. Indefinite causal structure results from combining probabilistic predictions and dynamical space-time. Combining the probabilistic nature of quantum theory and dynamical treatment space-time from general relativity is an approach to the problem of quantum gravity. The causaloid framework lays the mathematical groundwork to be able to treat indefinite causal structure. In this paper, we build on the causaloid mathematics and define a causally-unbiased entropy for an indefinite causal structure. In defining a causally-unbiased entropy, there comes about an emergent idea of causality in the form of a measure of causal connectedness, termed the Q factor.