Non-equilibrium and stochastic thermodynamics
Can escape times reveal hidden steps in an energy landscape?
Open access · cc by · source: Europe PMC
How quickly the fastest particles or molecules finish a journey reveals how many intermediate resting states they must pass through, and roughly how deep those states are.
Study at a glance
- Design
- Other — Colloidal particles diffusing in microchannels with optical-trap potential minima; first-passage time distributions compared with a network-theory prediction, then applied to two molecular datasets
- N
- Colloid datasets of 500 to 4000 trajectories each; nanopore hopper gave 161 two-hop and 87 three-hop events
- Population
- Polystyrene colloids in microfluidic channels; a DNA-cargo nanopore hopper; DNA hairpins in optical tweezers
- Outcome
- Short-time slope of the log-log first-passage time distribution and length of the power-law regime
Structured fields used in claim comparison tables when every cited study has a complete layer.
Key findings
At short times each distribution followed a power law whose integer slope equalled the number of intermediate minima crossed, as predicted by theory for networks of states. The duration of this power-law regime grew exponentially with trap depth, so it also encodes how deep the minima are. The nanopore hopper and the two DNA hairpins showed slopes of about 1 and 2, matching their known numbers of intermediate states, and the hopper data implied a well depth of about 17 kT.
Methodology
The authors trapped colloidal particles in narrow microfluidic channels and used holographic optical tweezers to place weak traps along them, creating known energy landscapes with one, two or three minima to cross. They measured how long particles took to exit (first-passage times) and plotted the distributions on log-log axes. They then applied the same analysis to existing data on a molecular hopper ratcheting DNA through a nanopore and on DNA hairpins folding and unfolding.
Limitations
The method recovers only the number and depth of minima along the shortest path, not the full shape of the landscape. It needs minima clearly deeper than thermal energy and good time resolution; shallow traps blurred the power law, and a slope counts only the minimum number of states, so shallower extra minima could be hidden. The m = 3 case for the nanopore had too few events to resolve, and the absence of a power law is hard to interpret.
How this study connects
Role on claims
Each row is a claim on a concept or method page where this paper supports, challenges, or qualifies the statement. Roles are hand-checked — not a model guess.
The timing of first arrivals can count hidden intermediate states.
For colloids crossing optical-trap landscapes, the short-time first-passage time distribution followed a power law whose integer slope equalled the number of intermediate minima; applied to a nanopore hopper and DNA hairpins, slopes of about 1 and 2 matched their known intermediate states.
Evidence for the claim as stated.
The timing of first arrivals can count hidden intermediate states.
For colloids crossing optical-trap landscapes, the short-time first-passage time distribution followed a power law whose integer slope equalled the number of intermediate minima; applied to a nanopore hopper and DNA hairpins, slopes of about 1 and 2 matched their known intermediate states.
Scope note — Recovers only the minimum number of states along the shortest path; needs minima clearly deeper than kT.
Limits the claim's scope: a different population, assay, or outcome.
The first-passage study is experimental and validated on real molecules, while the work-extraction and cavity results are simulations of idealised models; the latter show what the relations allow, not what is achieved in a lab.
Evidence for the claim as stated.
Open questions
Tensions this paper is part of
From concept pages' “where studies disagree.” Disagreement means the same question; scope means different assays, populations, or outcomes.
The first-passage study is experimental and validated on real molecules, while the work-extraction and cavity results are simulations of idealised models; the latter show what the relations allow, not what is achieved in a lab.
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