First-passage times in renewal and nonrenewal systems

Multicyclic Norias: A First-Transition Approach to Extreme Values of the Currents

For continuous-time Markov chains we prove that, depending on the notion of effective affinity F, the probability of an edge current to ever become negative is either 1 if F < 0 else ∼ exp - F . The result generalizes a "noria" formula to multicyclic networks. We give operational insights on the effective affinity and compare several estimators, arguing that stopping problems may be more accurate in assessing the nonequilibrium nature of a system according to a local observer. Finally we elaborate on the similarity with the Boltzmann formula. The results are based on a constructive first-transition approach.

Electron Waiting Times in a Strongly Interacting Quantum Dot: Interaction Effects and Higher-Order Tunneling Processes

Distributions of electron waiting times have been measured in several recent experiments and have been shown to provide complementary information compared with what can be learned from the electric current fluctuations. Existing theories, however, are restricted to either weakly coupled nanostructures or phase-coherent transport in mesoscopic conductors. Here, we consider an interacting quantum dot and develop a real-time diagrammatic theory of waiting time distributions that can treat the interesting regime, in which both interaction effects and higher-order tunneling processes are important. Specifically, we find that our quantum-mechanical theory captures higher-order tunneling processes at low temperatures, which are not included in a classical description, and which dramatically affect the waiting times by allowing fast tunneling processes inside the Coulomb blockade region. Our work paves the way for systematic investigations of temporal fluctuations in interacting quantum systems, for example close to a Kondo resonance or in a Luttinger liquid.

Kinetic uncertainty relation on first-passage time for accumulated current

The kinetic uncertainty relation (KUR) is a trade-off relation between the precision of an observable and the mean dynamical activity in a fixed time interval for a time-homogeneous and continuous-time Markov chain. In this Letter, we derive the KUR on the first passage time for the time-integrated current from the information inequality at stopping times. The relation shows that the precision of the first passage time is bounded from above by the mean number of jumps up to that time. We apply our result to simple systems and demonstrate that the activity constraint gives a tighter bound than the thermodynamic uncertainty relation in the regime far from equilibrium.

The thermodynamic uncertainty relation in biochemical oscillations

Living systems regulate many aspects of their behaviour through periodic oscillations of molecular concentrations, which function as 'biochemical clocks.' The chemical reactions that drive these clocks are intrinsically stochastic at the molecular level, so that the duration of a full oscillation cycle is subject to random fluctuations. Their success in carrying out their biological function is thought to depend on the degree to which these fluctuations in the cycle period can be suppressed. Biochemical oscillators also require a constant supply of free energy in order to break detailed balance and maintain their cyclic dynamics. For a given free energy budget, the recently discovered 'thermodynamic uncertainty relation' yields the magnitude of period fluctuations in the most precise conceivable free-running clock. In this paper, we show that computational models of real biochemical clocks severely underperform this optimum, with fluctuations several orders of magnitude larger than the theoretical minimum. We argue that this suboptimal performance is due to the small number of internal states per molecule in these models, combined with the high level of thermodynamic force required to maintain the system in the oscillatory phase. We introduce a new model with a tunable number of internal states per molecule and confirm that it approaches the optimal precision as this number increases.

Universal First-Passage-Time Distribution of Non-Gaussian Currents

We investigate the fluctuations of the time elapsed until the electric charge transferred through a conductor reaches a given threshold value. For this purpose, we measure the distribution of the first-passage times for the net number of electrons transferred between two metallic islands in the Coulomb blockade regime. Our experimental results are in excellent agreement with numerical calculations based on a recent theory describing the exact first-passage-time distributions for any nonequilibrium stationary Markov process. We also derive a simple analytical approximation for the first-passage-time distribution, which takes into account the non-Gaussian statistics of the electron transport, and show that it describes the experimental distributions with high accuracy. This universal approximation describes a wide class of stochastic processes, and can be used beyond the context of mesoscopic charge transport. In addition, we verify experimentally a fluctuation relation between the first-passage-time distributions for positive and negative thresholds.