The intersection of General Relativity and Quantum Mechanics suggests the possibility of nonlinearcausal structures, typically formalized as Closed Timelike Curves (CTCs). However, existingkinematic models suffer from logical ambiguities or exponential thermodynamic costs. In this work,we present a unified dynamic framework that resolves these pathologies through **DissipativeFeedback Control**. (I) We derive a Universal Contraction Theorem, proving that any non-linearquantum loop relaxes to a unique fixed point if the dissipation rate γ exceeds the feedback Lipschitzconstant K. We identify a thermodynamic phase transition between a stable ”Novikov phase”and a chaotic phase. (II) We analyze the computational complexity of this physically realizableregime, demonstrating that thermodynamic stability collapses the complexity class from PSPACEto BQP, thereby preserving the extended Church-Turing thesis. (III) We propose a concreteexperimental verification using interacting Rydberg polaritons in an EIT configuration, where thestable fixed point appears as a temporal soliton. This comprehensive study establishes non-linearquantum feedback not as a metaphysical anomaly, but as a testable branch of non-equilibriumthermodynamics.
The consistency of quantum mechanics in the presence of Closed Timelike Curves (CTCs) has traditionally been framed as a kinematic constraint. We propose a general dynamic framework where causal consistency emerges as a thermodynamic fixed point of open quantum systems. By modeling retrocausal loops as non-linear quantum channels with dissipation, we prove a Universal Contraction Theorem using the logarithmic norm of the Liouvillian superoperator. We demonstrate that any feedback system where the dissipation rate γ exceeds the non-linear Lipschitz constant K must relax to a unique, paradox-free state. We apply this framework to superconducting transmon qubits, deriving quantitative stability bounds (K < 10⁴ s⁻¹) testable with current FPGA technology. This work unifies the arrow of time with the Second Law of Thermodynamics, suggesting that causality is an emergent phase of non-equilibrium matter.
One out of many emerging implications from solutions of Einstein's general relativity equations are closed timelike curves (CTCs), which are trajectories through space-time 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 a solution through postselection. Both models are nonequivalent and imply nonstandard phenomena in the field of quantum computation and quantum mechanics. In this paper, 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 a decrease in entropy.
Born in the intersection between quantum mechanics and general relativity, indefinite causal structure is the idea that in the continuum of time, some sets of events do not have an inherent causal order between them. Process matrices, introduced by Oreshkov, Costa and Brukner (Nature Communications, 2012), define quantum information processing with indefinite causal structure -- a generalization of the operations allowed in standard quantum information processing, and to date, are the most studied such generalization.
Araujo et al. (Physical Review A, 2017) defined the computational complexity of process matrices, and showed that polynomial-time process matrix computation is equivalent to standard polynomial-time quantum computation with access to a weakening of post-selection Closed Timelike Curves (CTCs), that are restricted to be
linear. Araujo et al. accordingly defined the complexity class for efficient process matrix computation as
BQPℓCTC (which trivially contains
BQP), and posed the open question of whether
BQPℓCTC contains computational tasks that are outside
BQP.
In this work we solve this open question under a widely believed hardness assumption, by showing that
NP⊆BQPℓCTC. Our solution is captured by an even more restricted subset of process matrices that are purifiable (Araujo et al., Quantum, 2017), which (1) is conjectured more likely to be physical than arbitrary process matrices, and (2) is equivalent to polynomial-time quantum computation with access to
unitary (which are in particular linear) post-selection CTCs. Conceptually, our work shows that the previously held belief, that non-linearity is what enables CTCs to solve
NP, is false, and raises the importance of understanding whether purifiable process matrices are physical or not.
This paper presents a conceptual and analytical investigation into the limits of temporal access through the combined perspectives of causality, relativity, quantum mechanics, thermodynamics, and information theory. The work introduces the concept of the “Temporal Causality Barrier,” a selective and logically grounded framework that distinguishes between passive temporal observation and active temporal intervention. The paper argues that passive observation of the past is both physically permissible and continuously occurring through ordinary causal processes such as light propagation, memory, historical records, and astronomical observation. In contrast, active intervention into the past including backward information transfer, causal alteration of previous events, and closed causal loops is shown to generate logical contradictions and violations of causal consistency. The analysis critically examines major theoretical approaches related to time travel and retrocausality, including closed timelike curves, Novikov’s self-consistency principle, Deutsch’s quantum closed timelike curve model, and the two-state vector formalism in quantum mechanics. The paper argues that while some interpretations may mathematically describe retrocausal correlations, none currently provide an operational mechanism for backward information transmission without encountering paradoxes or information-theoretic inconsistencies. The framework further connects the causal structure of spacetime with the thermodynamic arrow of time, emphasizing the role of entropy, light cone geometry, and information propagation in preserving temporal coherence. The work also explores broader philosophical implications concerning the nature of time, consciousness, causality, and agency within a causally structured universe. Rather than proposing a new physical force or replacing existing theories, this paper provides a logically structured analysis of why temporal observation is compatible with known physics while active temporal intervention remains fundamentally constrained by both physical law and logical consistency.
Although general relativity allows the existence of closed timelike curves (CTCs), self-consistency problems arise (the ‘grandfather paradox’ among others). It is known that quantum mechanical consideration of the matter formally removes all the paradoxes, but the questions about causal structure remain. On the other hand, the idea of postselected CTCs (P-CTC) in quantum teleportation has know been put forward and experimentally implemented. We consider these problems with the aid of quantum causal analysis, where causality is defined without invoking the time relation. It implements the Cramer principle of weak causality, which admits time reversal in entangled states. We analyze Deutsch CTCs (D-CTC) with different kinds of interactions between the chronology-violating and chronology-respecting particles, with refined inferences about mixedness, quantum/classical correlations, entanglement and thermodynamics in the D-CTC. The main result is that time reversal causality can really exist, however, the final quantum state does not place retrospective constraints on the initial state, instead the final state can influence the state inside the D-CTC. This is effectively the implementation of Novikov self-consistency principle. The P-CTC has radically different properties; in particular, if the initial state was pure, the final state is always pure too. Self-consistency is controlled by the initial state-dependent traversability of the P-CTC.