The first-passage time is the natural observable of reaction completion, yet how its mean responds to a rate change has lacked a general constraint. We show that the logarithmic sensitivity of the mean first-passage time of any finite Markov chain to any rate is bounded by one in magnitude, and that these sensitivities sum to -1. Together the two laws form a conserved control budget: speeding completion through some transitions must be paid for by others, and a coordinated change shifts the completion time only as far as the budget allows. Raising an activation barrier or shifting the depth of a well moves many rates at once, yet neither can shift the completion time further than a single rate could. The budget caps kinetic-proofreading discrimination at the checkpoint count, and prices it in sensitivity to substrate concentration.
A simple symmetric random walk on a one-dimensional lattice is guaranteed to reach any target site, yet its mean first-passage time diverges. Here, we show that stochastic fluctuations in the jump rate can fundamentally alter this classic result. We find a phase transition in the mean first-passage time: sufficiently b...
The pace of evolution depends on how rapidly new phenotypes arise. We show that neutral Wright-Fisher evolution exhibits anomalous first passage despite diffusive mutations. The mean time for the first individual to reach a prescribed phenotypic distance scales approximately as $(\sigma^2)^{-3/2}$ with mutation varianc...
We study the first-passage time statistics of an active Ornstein--Uhlenbeck particle on a finite one-dimensional interval with an absorbing boundary at one end and a reflecting boundary at the other, subject to stochastic resetting. In the weak-activity regime, we develop a perturbative solution of the Fokker--Planck e...
Demosthenes K. Georgiou, P. Bressloff, Thibault Bertrand· 0 citations
We study the emergence of non-equilibrium steady states (NESS) in stochastic processes under threshold resetting, an event-driven protocol in which the system resets to its initial configuration upon crossing a prescribed spatial boundary (threshold). In contrast to externally driven resetting, whose steady-state prope...
We prove the existence of a non-trivial continuous stationary reversible dynamics on the directed landscape as a subsequential scaling limit of Brownian last passage percolation under the Ornstein--Uhlenbeck dynamics. Strong passage-time stability estimates from the companion paper Bhatia'26, together with static endpo...
In many soft-matter and biological systems, task completion relies on the cumulative arrival of multiple searchers rather than the speed of a single pioneer. The completion kinetics are therefore set not only by the first arrival, but by the full ordered sequence of first-passage times. Here, we determine how stochasti...
Ron Vatash, Eden Goldfarb, V. Rudyak et al.· 0 citations
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