We present a numerical simulation demonstrating that a self-referential quantum operation induces a directed, statistically robust monotonic growth of entanglement entropy in an observed subsystem. Drawing on the theoretical proposal that the arrow of time originates from directed information extraction within a quantum system , we design a minimal 4-qubit circuit initialized in the pure product state , so that subsystem starts with zero entanglement entropy. A self-referential layer, realized by controlled-NOT gates from subsystem to environment followed by randomization of , periodically extracts information from . Using IBM Qiskit's local simulator, we measure the entanglement entropy as a function of circuit depth. Under self-referential dynamics, exhibits a strongly significant monotonic trend (Spearman ), while two control circuits—one with symmetric - coupling () and one with reversed directional coupling ()—show significantly weaker or absent monotonicity. We discuss the limitations of interpreting this simulation as a full realization of thermodynamic irreversibility, and clarify that the observed monotonic entropy increase is a necessary but not sufficient condition for a genuine arrow of time. This work provides a minimal, accessible testbed for exploring the information-theoretic origins of temporal irreversibility .
We present a numerical simulation demonstrating that a self-referential quantum operation induces a directed, statistically robust monotonic growth of entanglement entropy in an observed subsystem. Drawing on the theoretical proposal that the arrow of time originates from directed information extraction within a quantum system , we design a minimal 4-qubit circuit initialized in the pure product state , so that subsystem starts with zero entanglement entropy. A self-referential layer, realized by controlled-NOT gates from subsystem to environment followed by randomization of , periodically extracts information from . Using IBM Qiskit's local simulator, we measure the entanglement entropy as a function of circuit depth. Under self-referential dynamics, exhibits a strongly significant monotonic trend (Spearman ), while two control circuits—one with symmetric - coupling () and one with reversed directional coupling ()—show significantly weaker or absent monotonicity. We discuss the limitations of interpreting this simulation as a full realization of thermodynamic irreversibility, and clarify that the observed monotonic entropy increase is a necessary but not sufficient condition for a genuine arrow of time. This work provides a minimal, accessible testbed for exploring the information-theoretic origins of temporal irreversibility .
A central question in the quantum-gravitational description of our universe is how the arrow of time emerges from a fundamentally timeless theory. Reference [1] proposed that an intrinsic, self-referential mechanism—encoded in a nonlocal operator acting on a holographic tensor network—breaks the global Wheeler-DeWitt constraint and drives the monotonic growth of entanglement entropy, thereby giving rise to an internal time. The present work provides the first exactly solvable and numerically testable microscopic realization of this mechanism within the open Sachdev-Ye-Kitaev (SYK) model. By interpreting Lindblad jump operators as directed information extractions from network degrees of freedom, we prove, via large- Schwinger-Keldysh field theory and finite- exact diagonalization (up to ), that the entanglement entropy of the observed subsystem increases monotonically and irreversibly, that the level-spacing distribution transitions from Poisson to Wigner-Dyson universality, and that the dissipative form factor displays a sharp, first-order dynamical phase transition. A control experiment employing structureless, nonlocal Lindblad jumps fails to produce these signatures simultaneously, confirming that they are specific consequences of the self-referential mapping rather than generic features of open quantum systems. We further propose a holographic dictionary in which the dissipative coupling is dual to the boundary cosmological constant in Jackiw-Teitelboim gravity, offering a concrete, testable bridge between the self-referential operation and the geometry of emergent spacetime. These findings establish a compact, computable, and—crucially—experimentally accessible microscopic foundation for the hypothesis that time is born from quantum information processing, and they provide a theoretical blueprint for observing the emergence of an arrow of time on near-term quantum simulators.
A central question in the quantum-gravitational description of our universe is how the arrow of time emerges from a fundamentally timeless theory. Reference proposed that an intrinsic, self-referential mechanism—encoded in a nonlocal operator acting on a holographic tensor network—breaks the global Wheeler-DeWitt constraint and drives the monotonic growth of entanglement entropy, thereby giving rise to an internal time. The present work provides the first exactly solvable and numerically testable microscopic realization of this mechanism within the open Sachdev-Ye-Kitaev (SYK) model. By interpreting Lindblad jump operators as directed information extractions from network degrees of freedom, we prove, via large- Schwinger-Keldysh field theory and finite- exact diagonalization (up to ), that the entanglement entropy of the observed subsystem increases monotonically and irreversibly, that the level-spacing distribution transitions from Poisson to Wigner-Dyson universality, and that the dissipative form factor displays a sharp, first-order dynamical phase transition. A control experiment employing structureless, nonlocal Lindblad jumps fails to produce these signatures simultaneously, confirming that they are specific consequences of the self-referential mapping rather than generic features of open quantum systems. We further propose a holographic dictionary in which the dissipative coupling is dual to the boundary cosmological constant in Jackiw-Teitelboim gravity, offering a concrete, testable bridge between the self-referential operation and the geometry of emergent spacetime. These findings establish a compact, computable, and—crucially—experimentally accessible microscopic foundation for the hypothesis that time is born from quantum information processing, and they provide a theoretical blueprint for observing the emergence of an arrow of time on near-term quantum simulators .
The contradiction between the thermodynamic arrow of time and microscopic dynamical reversibility is a core problem in statistical physics. Within the framework of connectivity engineering, this paper proposes a new mechanism: irreversible accumulation of subsystem entropy caused by topological quenching. We numerically simulate the cyclic switching of a one-dimensional spin network between topological steps k=1 and k=4. Results show that each switch from the highly connected state to the frustrated state leads to an irreversible "fall" of information into the local entanglement space; when switched back to the initial topology, the subsystem entanglement entropy cannot recover to its initial value, but instead surges from 0 to approximately 2.96 and remains in the saturation regime, exhibiting a unidirectional entropy accumulation. Since the theoretical maximum entropy of this subsystem is 3.0, this irreversible saturation directly reveals the limit of information coarse-graining. The above results prove that the microscopic origin of the arrow of time is precisely the information scrambling caused by the irreversibility of underlying geometric topological reconstruction.
The origin of the macroscopic arrow of time remains one of the most profound puzzles in theoretical physics, traditionally tied to the monotonic increase of total entropy dictated by the second law of thermodynamics. In this work, we propose and rigorously analyze the concept of the Quantum Thermodynamic Arrow Inverter (QTAI), a theoretical framework designed within open quantum systems where a local subsystem can exhibit a transient or sustained decrease in local entropy, characterized mathematically by d S_sub / dt < 0, while the global composite system strictly satisfies the global second law of thermodynamics, given by d S_total / dt >= 0. Rather than focusing merely on conventional cooling or refrigeration cycles, QTAI investigates whether the thermodynamic arrow of time can be dynamically and non-trivially redistributed across entangled and correlated quantum sub-degrees of freedom. By leveraging non-Markovian system-environment interactions, quantum coherence, and information-theoretic resource allocation, we demonstrate that different subsystems can effectively experience distinct local temporal directions or asymmetric thermodynamic aging. This paradigm introduces the Arrow of Time Redistribution as a fundamental principle, potentially bridging quantum information theory, open system dynamics, and the foundational nature of time itself.
This work investigates the fundamental connection between quantum mechanics and thermodynamics through the concept of the arrow of time. While the second law of thermodynamics identifies the arrow of time with the monotonic increase of entropy in isolated systems, closed quantum systems evolve unitarily and conserve von Neumann entropy, making the origin of irreversibility less apparent. Here we establish a no-go theorem proving that correlations in unknown states of closed quantum systems cannot be universally removed by any physical operation. This result demonstrates that correlation generation is inherently irreversible, providing a microscopic and universal basis for the arrow of time. In thermodynamic settings, this irreversibility ensures that heat flows spontaneously from hotter to colder subsystems, reproducing the Clausius formulation of the second law. More generally, the irreversible growth of correlations explains entropy increase, the approach to equilibrium, and decoherence as observable manifestations of the same principle. Our findings ground a quantum-mechanical foundation for the second law of thermodynamics and demonstrate the universality of the arrow of time.
The concept of time presents a profound challenge at the intersection of quantum mechanics and thermodynamics. While fundamental microscopic laws are largely time-symmetric, macroscopic phenomena universally exhibit a distinct thermodynamic arrow of time, characterized by increasing entropy. This paper explores the hypothesis that quantum entanglement plays a crucial role in the emergence of this thermodynamic arrow. We review how the entanglement between a quantum system and its environment leads to decoherence, effectively driving the system towards a state of higher entropy and classical-like behavior. By analyzing concepts such as von Neumann entropy, entanglement entropy, and the Page-Wootters mechanism, we propose a theoretical framework where the degradation and spreading of entanglement act as the underlying mechanism for the perceived unidirectional flow of time. This approach offers a potential resolution to the "problem of time" in quantum gravity and provides a unified perspective on the genesis of irreversibility from the inherently reversible laws of quantum mechanics. We discuss the implications of this entanglement-driven temporal emergence for our understanding of the universe's initial low-entropy state and the fundamental nature of reality.