Recent work on quantum collapse models suggests that stochastic collapse dynamics can induce an intrinsic contribution to clock-time uncertainty, which can be interpreted as an effective fundamental (though extremely small) limit on clock precision. Here we investigate the operational consequences of such time uncertainty for reversibility and the thermodynamic arrow of time. We model fundamental time noise as a Brownian jitter of the effective time parameter in a driven quantum system and study its impact on Loschmidt echo, entropy production, and the depth of reversible control protocols. Using a minimal two-qubit model we show that even arbitrarily weak time noise leads to (i) a systematic decay of the Loschmidt echo, (ii) monotonic entropy growth under ensemble averaging, and (iii) a finite reversibility horizon Nc(Θ) that scales approximately as Nc ∝ Θ−1 with the time–noise strength Θ. We interpret these results in the framework of relational and operational time: fundamental time uncertainty manifests itself as a finite temporal budget of usable, low-entropy correlations and induces an intrinsic limit on the depth of reversible dynamics.
Recent work on quantum collapse models suggests that stochastic collapse dynamics can induce an intrinsic contribution to clock-time uncertainty, which can be interpreted as an effective fundamental (though extremely small) limit on clock precision. Here we investigate the operational consequences of such time uncertainty for reversibility and the thermodynamic arrow of time. We model fundamental time noise as a Brownian jitter of the effective time parameter in a driven quantum system and study its impact on Loschmidt echo, entropy production, and the depth of reversible control protocols. Using a minimal two-qubit model we show that even arbitrarily weak time noise leads to (i) a systematic decay of the Loschmidt echo, (ii) monotonic entropy growth under ensemble averaging, and (iii) a finite reversibility horizon Nc(Θ) that scales approximately as Nc ∝ Θ−1 with the time–noise strength Θ. We interpret these results in the framework of relational and operational time: fundamental time uncertainty manifests itself as a finite temporal budget of usable, low-entropy correlations and induces an intrinsic limit on the depth of reversible dynamics.
In this work, the origin of the Arrow of Time is explored within the framework of Timeless Correlation Theory (TCT), based on the relational Page–Wootters formalism. In this operational approach, time is represented by a finite “System–Clock” setup, and irreversibility is treated as a property of concrete time-reversal protocols (Loschmidt echoes) in the presence of noise. It is shown that the breakdown of quantum reversibility is driven not only by thermodynamic entropy, but also by dynamic control fragility — the accumulation of small systematic errors in a finite number of control operations. Key results: A new rule for quantum control (The N–rule). The reversibility of the Loschmidt echo is comparatively robust to incoherent (thermodynamic) noise, yet catastrophically sensitive to systematic control errors. This fragility is governed primarily by the number of operations N, rather than by the total evolution time τ, which gives the Arrow of Time a fundamentally operational character. Dynamic Robustness Mode. A paradoxical regime is identified in which coarsening the clock step (larger Δt at fixed N) slows down the decay of the Loschmidt echo and makes the reversal protocol more robust. This suggests a nontrivial strategy for error mitigation in quantum control and quantum computing. Temporal budget concept. The work introduces the notion of a finite “temporal budget” for noisy clocks — a limited entropic resource of System–Clock correlations. Within TCT, thermodynamic irreversibility arises when this budget is exhausted due to accumulated decoherence. Taken together, the results unify thermodynamic and dynamic aspects of time into a single relational picture: thermodynamic noise sets the size of the available temporal budget, while dynamic control fragility determines the rate at which it is spent. The work should be viewed as a preliminary theoretical framework and remains under active development.
Fluctuations are intrinsic to microscopic systems and impose fundamental limits on nonequilibrium precision, as captured by the thermodynamic uncertainty relation (TUR), which links current fluctuations to entropy production. While feedback control is expected to further suppress fluctuations, its role within the TUR framework has remained unclear, particularly in quantum systems where control is inherently information-driven. In this Letter, we consider open quantum systems weakly coupled to a thermal environment, in which quantum jumps are continuously monitored, and Markovian feedback is applied. Using quantum mutual information to quantify the information contribution induced by feedback, we derive a finite-time TUR for arbitrary time-integrated currents in terms of entropy production and mutual information. Our results uncover how feedback control suppresses fluctuations together with thermodynamic cost and establish a fundamental precision bound imposed by information-based control. As an application, we analyze a quantum clock model and demonstrate that the clock precision can be enhanced by feedback control in the presence of a single thermal reservoir.
Entropy production characterizes irreversibility. This viewpoint allows us to consider the thermodynamic uncertainty relation, which states that a higher precision can be achieved at the cost of higher entropy production, as a relation between precision and irreversibility. Considering the original and perturbed dynamics, we show that the precision of an arbitrary counting observable in continuous measurement of quantum Markov processes is bounded from below by the Loschmidt echo between the two dynamics, representing the irreversibility of quantum dynamics. When considering particular perturbed dynamics, our relation leads to several thermodynamic uncertainty relations, indicating that our relation provides a unified perspective on classical and quantum thermodynamic uncertainty relations.
Abstract In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relations under open systems, and how to steer the uncertainty under different types of decoherence. Specifically, we develop the dynamical behaviors of the uncertainty of interest under two typical categories of noise; bit flipping and depolarizing channels. It has been shown that the measurement uncertainty firstly increases and then decreases with the growth of the decoherence strength in bit flipping channels. In contrast, the uncertainty monotonically increases with the increase of the decoherence strength in depolarizing channels. Notably, and to a large degree, it is shown that the uncertainty depends on both the systematic quantum correlation and the minimal conditional entropy of the observed subsystem. Moreover, we present a possible physical interpretation for these distinctive behaviors of the uncertainty within such scenarios. Furthermore, we propose a simple and effective strategy to reduce the entropic uncertainty by means of a partially collapsed operation—quantum weak measurement. Therefore, our investigations might offer an insight into the dynamics of the measurment uncertainty under decoherence, and be of importance to quantum precision measurement in open systems.
Even though our microscopic physical theories, such as classical or quantum mechanics, are time-reversal invariant, time appears to march forward irreversibly. It is widely believed that effective entropy increase due to the second law of thermodynamics is at the origin of this emergent arrow of time. Any system that is out of thermal equilibrium and produces entropy can thus be used as a clock, be it a melting ice cube or a sophisticated atomic clock. The understanding of entropy in physics has significantly advanced with the advent of information theory in the last century. It has also led to the insight that the amount of entropy a clock produces is linked to how precisely the clock works, and thereby, how much information the clock reveals about the passage of time. In this thesis, we ask: what fundamental limits does the underlying physical theory impose on the precision of clocks within that theory? To rigorously answer this question, we devise a minimal clock model within quantum theory. By consistently modeling all clock constituents as quantum systems, we can ensure we account for all the resources used by the clock. This includes, in particular, the readout. Classically, one can obtain this for free, but quantum mechanically, this has a resource cost associated with it. To this end, we consolidate existing frameworks that describe clocks in both classical and quantum theory. Revising fluctuation theorems from quantum thermodynamics, we demonstrate how such theorems impose limits on the attainable precision of clocks. These precision bounds turn out to be more stringent for classical systems than for quantum ones. Quantum clocks can harness coherence and correlations to suppress fluctuations, allowing them to exponentially surpass precision bounds that hold for classical clocks. We show this separation between classical and quantum clocks by constructing an explicit example that uses quantum dynamics to saturate the quantum precision bounds. Finally, we close the thesis by exploring implications of these timekeeping bounds beyond fundamental science in quantum technologies. We show how quantum clocks can be used to quantify the energetic cost of quantum computation by linking computational fidelity to thermodynamic entropy production.
In 1964, Yu. A. Gol'fand proposed an extension of quantum mechanics to discrete time, predicting intrinsic non-unitarity and entropy increase. While historically significant, this formalism predates the modern theory of open quantum systems. In this work, we rigorously recast Gol'fand's discrete evolution equation as a Completely Positive Trace-Preserving (CPTP) quantum channel and derive its continuous-time coarse-grained limit. We demonstrate that the dynamics converge to a specific Lindblad master equation characterized by a fundamental time scale τ, which induces decoherence in both the energy basis and a fundamental operator basis W. We analyze the thermodynamic implications using Spohn's entropy production formalism, proving that the discrete time step induces a strictly positive entropy production rate driven by the decay of quantum coherences, thereby providing a microscopic foundation for the arrow of time independent of environmental coupling. Furthermore, we quantify the loss of quantum coherence via fidelity decay and purity loss, establishing exact constraints for fault-tolerant quantum computing. We further investigate the impact of this intrinsic decoherence on Discrete Time Crystals (DTCs), showing that Gol'fand dynamics impose a fundamental lifetime limit on time-translation symmetry breaking phases. Finally, we utilize precision data from optical lattice clocks, matter-wave interferometry, and neutrino oscillations to place stringent upper bounds on τ. Our results constrain the fundamental time discretization to τ≲10−26 s, significantly tightening previous limits and offering a testable framework for quantum gravity phenomenology.