44 research outputs found
Early Stages of Homopolymer Collapse
Interest in the protein folding problem has motivated a wide range of
theoretical and experimental studies of the kinetics of the collapse of
flexible homopolymers. In this Paper a phenomenological model is proposed for
the kinetics of the early stages of homopolymer collapse following a quench
from temperatures above to below the theta temperature. In the first stage,
nascent droplets of the dense phase are formed, with little effect on the
configurations of the bridges that join them. The droplets then grow by
accreting monomers from the bridges, thus causing the bridges to stretch.
During these two stages the overall dimensions of the chain decrease only
weakly. Further growth of the droplets is accomplished by the shortening of the
bridges, which causes the shrinking of the overall dimensions of the chain. The
characteristic times of the three stages respectively scale as the zeroth, 1/5
and 6/5 power of the the degree of polymerization of the chain.Comment: 11 pages, 3 figure
Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
In the context of Markov evolution, we present two original approaches to
obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the
language of stochastic derivatives and by using a family of exponential
martingales functionals. We show that GFDT are perturbative versions of
relations verified by these exponential martingales. Along the way, we prove
GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the
usual proof for diffusion and pure jump processes. Finally, we relate the FR to
a family of backward and forward exponential martingales.Comment: 41 pages, 7 figures; version2: 45 pages, 7 figures, minor revisions,
new results in Section
Quantum Fluctuation Relations for the Lindblad Master Equation
An open quantum system interacting with its environment can be modeled under
suitable assumptions as a Markov process, described by a Lindblad master
equation. In this work, we derive a general set of fluctuation relations for
systems governed by a Lindblad equation. These identities provide quantum
versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response
regime, these fluctuation relations yield a fluctuation-dissipation theorem
(FDT) valid for a stationary state arbitrarily far from equilibrium. For a
closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula