878 research outputs found
Large-deviation theory for a Brownian particle on a ring: a WKB approach
We study the large deviation function of the displacement of a Brownian
particle confined on a ring. In the zero noise limit this large deviation
function has a cusp at zero velocity given by the Freidlin-Wentzell theory. We
develop a WKB approach to analyse how this cusp is rounded in the weak noise
limit
Discrete-time thermodynamic uncertainty relation
We generalize the thermodynamic uncertainty relation, providing an entropic
upper bound for average fluxes in time-continuous steady-state systems
(Gingrich et al., Phys. Rev. Lett. 116, 120601 (2016)), to time-discrete Markov
chains and to systems under time-symmetric, periodic driving
Phase transitions in persistent and run-and-tumble walks
We calculate the large deviation function of the end-to-end distance and the
corresponding extension-versus-force relation for (isotropic) random walks, on
and off-lattice, with and without persistence, and in any spatial dimension.
For off-lattice random walks with persistence, the large deviation function
undergoes a first order phase transition in dimension . In the
corresponding force-versus-extension relation, the extension becomes
independent of the force beyond a critical value. The transition is anticipated
in dimensions and , where full extension is reached at a finite
value of the applied stretching force. Full analytic details are revealed in
the run-and-tumble limit. Finally, on-lattice random walks with persistence
display a softening phase in dimension and above, preceding the usual
stiffening appearing beyond a critical value of the force
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