# A Universal Control Budget for First-Passage Kinetics

Source: [A Universal Control Budget for First-Passage Kinetics](<https://www.sota2.com/research/paper/6a7566c0a080ff033d3e2b39>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-08-14T05:00:04.744Z

Authors: Shiling Liang, Ruicheng Bao

Published: 2026-08-06T17:58:06.000Z

## Abstract

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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2608.06368>)

[PDF](<https://arxiv.org/pdf/2608.06368.pdf>)