Constraints on Reversing the Thermodynamic Arrow of Time from Black Hole Thermodynamics, Wormholes, and Time-Symmetric Quantum Mechanics
Kevin Song, John Zhang
TL;DR
The paper analyzes whether the thermodynamic arrow of time can be reversed within a single connected universe by leveraging black holes, traversable wormholes, and time-symmetric quantum frameworks. It introduces the Global Entropy Transport (GET) framework and derives sectoral bounds that constrain how matter and radiation entropies can be reduced without increasing generalized entropy $S_{\mathrm{gen}}$; horizon area and correlation terms must compensate any local decreases. Key tools include the generalized entropy $S_{\mathrm{gen}} = \frac{A}{4 G \hbar} + S_{\mathrm{out}}$, quantum focusing, QNEC, QFC, and island-based Page curve calculations, all of which uphold a nondecreasing $S_{\mathrm{gen}}$ in semiclassical gravity. The analysis shows that black holes, wormholes, and retrocausal protocols can redistribute entropy but cannot operationally reverse the universal entropy arrow in a single universe, though they can create intricate, local entropy patterns constrained by holographic and information-theoretic limits. This work thus reinforces the robustness of the cosmological arrow of time under semiclassical dynamics and clarifies the role of holography and quantum information in entropy transport.
Abstract
Can the thermodynamic arrow of time in a single universe be reversed, even temporarily, within semiclassical gravity without invoking additional universes or branches? We address this question in a single, connected spacetime where quantum field theory is coupled to classical general relativity, and where black holes, traversable wormholes, and time-symmetric or retrocausal formulations of quantum mechanics might naively appear to open channels for entropy export or cancellation. After distinguishing fine-grained, coarse-grained, and generalized gravitational entropy, and formulating a cosmological coarse-grained entropy, we treat black hole evaporation, wormholes constrained by quantum energy inequalities, and two-time boundary-value frameworks (including absorber-type and two-state-vector formalisms) within a common information-theoretic language. We then introduce a "Global Entropy Transport" (GET) framework and derive a sectoral inequality that bounds the net decrease of matter-plus-radiation entropy in terms of changes in horizon area and correlation (mutual-information) terms, assuming the generalized second law and modern focusing and energy conditions. Within this framework, black holes, wormholes, and retrocausal protocols can at most redistribute entropy among matter, radiation, and gravitational sectors and reshape the local pattern of entropy production. They do not, under current semiclassical, holographic, and statistical-mechanical constraints, permit a genuine reversal of the universal thermodynamic arrow in a single connected universe.