  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.
