Thermodynamic Constraints on Closed Timelike Curves from Unified Quantum Gravity

Here, we derive thermodynamic constraints on closed timelike curves (CTCs) within the framework of Unified Quantum Gravity (UQG). By analyzing the entropy evolution along worldlines in spacetimes known to contain CTCs (Gödel universe, extremal Kerr black holes, and Alcubierre warp drives), we demonstrate that all such configurations violate the second law of thermodynamics. The key result is that CTCs require dS/dt = 0 everywhere along the worldline (reversible process), while all physical processes are irreversible (dS/dt > 0). This provides a concrete thermodynamic mechanism for Hawking's chronology protection conjecture. We show that the grandfather paradox is forbidden by entropy increase, and compute the entropy cost of time travel to be ΔS ~ 10^27 J/K per year. Our results confirm that time travel is thermodynamically impossible in realistic scenarios, with the Hubble parameter relation H ∝ dS/dt serving as the fundamental constraint. These findings are testable through astrophysical observations and provide falsifiable predictions for quantum gravity phenomenology.