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.
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.
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.
Recent proposals regarding Closed Timelike Curves (CTCs) suggest they could efficiently solve NP-complete problems. However, we have previously demonstrated that physical CTCs must be dissipative to satisfy the Novikov Self-Consistency Principle. In this work, we derive the computational consequences of this thermodynamic stability. We introduce Geometric Causal Complexity (GCC), a measure based on the accessible volume of the Hilbert space under the Fubini-Study metric. We prove a Universal Causal Complexity Bound: the computational advantage ΔC of a retrocausal channel is strictly limited by the ratio of non-linearity to dissipation, ΔC ≤ (K/γ) C_max. This implies that the "Arrow of Time" acts as a computational resource constraint: the same mechanism that prevents logical paradoxes also prevents the violation of the Church-Turing thesis. We analyze the implications for Rydberg atoms, superconducting circuits, and photonic networks, classifying them by their potential for non-Markovian quantum advantage.
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.
Deriving the laws of thermodynamics from an underlying microscopic picture is a central quest of statistical mechanics. The present article focuses on the derivation of the first and second law of thermodynamics for closed and open quantum systems, where such foundational questions in addition become practically relevant for emergent nanotechnologies. Recent progress is presented in a self-contained way, with an emphasis on general ideas and useful tools instead of particular applications. We identify limits and conceptual shortcomings of previous approaches. Then, we propose a novel, unifying perspective, which starts from a microscopic definition of nonequilibrium thermodynamic entropy. The change of this entropy is identified with the entropy production, which satisfies a fluctuation theorem for a large class of initial states. Moreover, this entropy production can be naturally separated into a quantum and a classical component. Within our framework, we introduce the notions of recoverable work and remaining heat. In the case of a weakly perturbed ideal thermal bath this approach is in quantitative agreement with previous ones, thus ensuring their thermodynamic consistency.
The nonlinear equation of motion that accomplishes a self-consistent unification of quantum mechanics (QM) and thermodynamics conceptually different from the (von Neumann) foundations of quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but which reduces to the same mathematics for the thermodynamic equilibrium (TE) states, and contains standard QM in that it reduces to the time-dependent Schrodinger equation for zero entropy states is discussed in full mathematical detail. By restricting the discussion to a strictly isolated system (noninteracting, disentangled and uncorrelated), we show how the theory departs from the conventional QSM/QIT rationalization of the second law of thermodynamics, which instead emerges in QT (quantum thermodynamics) as a theorem of existence and uniqueness of a stable equilibrium state for each set of mean values of the energy and the number of constituent particles. To achieve this, the theory assumes Trρ lnρ B −k for the physical entropy and is designed to implement two fundamental ansatzs: (1) that in addition to the standard QM states described by idempotent density operators (zero entropy), a strictly isolated and uncorrelated system admits also states that must be described by non-idempotent density operators (nonzero entropy); (2) that for such additional states the law of causal evolution is determined by the simultaneous action of a Schrodinger-von Neumann-type Hamiltonian generator and a nonlinear dissipative generator which conserves the mean values of the energy and the number of constituent particles, and in forward time drives the density operator in the 'direction' of steepest entropy ascent (maximal entropy generation). The resulting dynamics is well defined for all non-equilibrium states, no matter how far from TE. Existence and uniqueness of solutions of the Cauchy initial value problem for all density operators implies that the equation of motion can be solved not only in forward time, to describe relaxation towards TE, but also in backward time, to reconstruct the 'ancestral' or primordial lowest entropy state or limit cycle from which the system originates. Zero entropy states as well as a well defined family of non-dissipative states evolve unitarily according to pure Hamiltonian dynamics and can be viewed as unstable limit cycles of the general nonlinear dynamics.
We discuss and motivate the form of the generator of a nonlinear quantum dynamical group 'designed' so as to accomplish a unification of quantum mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum Thermodynamics (QT). Its conceptual foundations differ from those of (von Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the same mathematics, and for zero entropy states it reduces to standard unitary QM. The nonlinear dynamical group of QT is construed so that the second law emerges as a theorem of existence and uniqueness of a stable equilibrium state for each set of mean values of the energy and the number of constituents. It implements two fundamental ansatzs. The first is that in addition to the standard QM states described by idempotent density operators (zero entropy), a strictly isolated system admits also states that must be described by non-idempotent density operators (nonzero entropy). The second is that for such additional states the law of causal evolution is determined by the simultaneous action of a Schroedinger-von Neumann-type Hamiltonian generator and a nonlinear dissipative generator which conserves the mean values of the energy and the number of constituents, and (in forward time) drives any density operator, no matter how far from TE, in the 'direction' of steepest entropy ascent (maximal entropy increase). The equation of motion can be solved not only in forward time, to describe relaxation towards TE, but also backwards in time, to reconstruct the 'ancestral' or primordial lowest entropy state or limit cycle from which the system originates.