For highly unstable potentials, the long-time distribution of trajectories conditioned to never diverge is light-tailed, while the quasi-stationary distribution of trajectories surviving to a fixed time is heavy-tailed with an exponent set by the potential's divergent term.
Exact Distributions of Currents and Frenesy for Markov Bridges
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abstract
We consider discrete-time Markov bridges, chains whose initial and final states coincide. We derive exact finite-time formulae for the joint probability distributions of additive functionals of trajectories. We apply our theory to time-integrated currents and frenesy of enzymatic reactions, which may include absolutely irreversible transitions. We discuss the information that frenesy carries about the currents and show that bridges may violate known uncertainty relations in certain cases. Numerical simulations are in perfect agreement with our theory.
fields
cond-mat.stat-mech 1years
2019 1verdicts
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Living on the edge of instability
For highly unstable potentials, the long-time distribution of trajectories conditioned to never diverge is light-tailed, while the quasi-stationary distribution of trajectories surviving to a fixed time is heavy-tailed with an exponent set by the potential's divergent term.