This work proposes an original formulation that establishes a rigorous mathematical correspondence between the quantum arrow of time, emerging from decoherence and measurement processes, and the thermodynamic arrow of time, associated with the increase in entropy. The central thesis is that these two arrows are not independent phenomena, but different manifestations of a single fundamental principle of quantum information dissipation.
This work proposes an original formulation that establishes a rigorous mathematical correspondence between the quantum arrow of time, emerging from decoherence and measurement processes, and the thermodynamic arrow of time, associated with the increase in entropy. The central thesis is that these two arrows are not independent phenomena, but different manifestations of a single fundamental principle of quantum information dissipation.
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.
The problem of time’s arrow is (roughly) to understand why macroscopic physical processes typically evolve in a specific direction (the one we call “the future”) even though the underlying laws of physics describing the individual microscopic systems are time-reversal invariant. The standard answer to this problem is given by Boltzmann’s explanation of the II law of thermodynamics: a classical system starting in a non-equilibrium state spontaneously (i.e. with a high level of probability) tends towards equilibrium, thus implementing an irreversible process. However, this explanation has two drawbacks: 1. it needs a further assumption on the entropy of the initial state of the universe (past hypothesis); 2. microscopic systems (e.g. molecules in a box) should be represented as quantum states and not classical states. In this talk, I want to propose a different hypothesis to explain the origin of time’s arrow, based on quantum mechanics, specifically on decoherence theory. Differently from isolated systems, open quantum systems described by decoherence theory showirreversible behavior, as they evolve towards decoherence and von Neumann entropy increase. Is this behavior a sign of genuine irreversibility? And, if so, can this be linked to thermodynamic irreversibility?
The arrow-of-time dilemma states that the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e., entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.
This work explores the hypothesis that time is an emergent phenomenon arising from underlying quantum informational processes. By integrating principles from quantum mechanics, thermodynamics, and general relativity, we develop a comprehensive framework that elucidates the relationship between quantum complexity, entanglement, and the nature of time. We investigate the role of quantum complexity in the evolution of quantum states and demonstrate how the increase in entanglement entropy provides a microscopic basis for the arrow of time. Using the AdS/CFT correspondence and the holographic principle, we establish connections between spacetime geometry and quantum informational measures like entanglement entropy. We address the black hole information paradox within this context, arguing that information is preserved in a highly scrambled form. Additionally, we propose an experimental design using black hole analogues to empirically validate our theoretical predictions, focusing on fast scrambling and the growth of quantum complexity. Our findings suggest that quantum informational dynamics govern the emergence of time and spacetime geometry. This work bridges quantum mechanics, thermodynamics, information theory, and general relativity, offering potential applications in quantum technologies and new insights into the fundamental nature of reality.
Abstract:Building upon the analytic quantum thermodynamic framework I previously established (Zou, 2025), this article presents a discrete ontological model in which the arrow of time emerges from irreversible energy transfers driven by local energy gradients on a topologically fixed spatial network, with the temporal sequence identified as the successive updates of spatial energy redistribution. A multiplicative entropy, defined as the product of all node energies, increases exactly with every transfer, providing a non-statistical, step-by-step measure of temporal progression. I argue that energy dissipation is fundamentally identical to decoherence: the former supplies the physical mechanism, the latter the observational signature. This framework synthesizes three intellectual traditions—computational time (Wolfram, 't Hooft), gradient-driven thermodynamics (Annila), and decoherence (Joos & Zeh, Kiefer)—into a unified picture where time is the counting of irreversible energy redistribution on discrete space.