Closed timelike curves and the second law of thermodynamics

TL;DR

This paper explores how closed timelike curves (CTCs) in quantum models can lead to violations of the second law of thermodynamics by constructing quantum circuits that decrease entropy.

Contribution

It analyzes the implications of Deutsch's and Bennett-Schumacher's CTC models on thermodynamics, showing potential entropy decrease in quantum circuits.

Findings

CTC-based quantum circuits can decrease entropy.

Different quantum CTC models have distinct implications.

Potential violations of the second law in quantum contexts.

Abstract

One out of many emerging implications from solutions of Einstein's general relativity equations are closed timelike curves (CTCs), which are trajectories through spacetime that allow for time travel to the past without exceeding the speed of light. Two main quantum models of computation with the use of CTCs were introduced by Deutsch (D-CTC) and by Bennett and Schumacher (P-CTC). Unlike the classical theory in which CTCs lead to logical paradoxes, the quantum D-CTC model provides a solution that is logically consistent due to the self-consistency condition imposed on the evolving system, whereas the quantum P-CTC model chooses such solution through post-selection. Both models are non-equivalent and imply nonstandard phenomena in the field of quantum computation and quantum mechanics. In this work we study the implications of these two models on the second law of thermodynamics - the fundamental principle which states that in an isolated system the entropy never decreases. In particular, we construct CTC-based quantum circuits which lead to decrease of entropy.