arXiv subjects

Patrick Malsom

Publications and source records attributed to Patrick Malsom.

2 recordsLinked to original sources

arXiv2017

Pinned Brownian Bridges in the Continuous-Time Limit

The current understanding of pinned Brownian bridges is based on the Onsager-Machlup (OM) functional. The continuous-time limit of the OM functional can be expressed either by using the Fokker-Planck equation or by using the Radon-Nikodym derivative with the help of the Girsanov theorem and Ito's lemma. The resulting expression, called here, the Ito-Girsanov (IG) measure, has been used as a basis of algorithms designed to create ensembles of transition paths, paths that are constrained to start in one free energy basin and end in another. Here we explore the underlying formalism and show that the IG measure originates in an expression that is only conditionally convergent. Thus without a sound mathematical foundation, the IG measure produces unphysical results when used in computer algorithms that are designed to elucidate chemical transitions.

cond-mat.stat-mech↗

arXiv2015

Rare Events, the Thermodynamic Action and the Continuous-Time Limit

We consider diffusion-like paths that are explored by a particle moving via a conservative force while being in thermal equilibrium with its surroundings. To probe rare transitions, we use the Onsager-Machlup (OM) functional as a path probability distribution function for double-ended paths that are constrained to start and stop at predesignated points after a fixed time. We explore the continuous-time limit where the OM functional has been commonly regularized by using the Ito-Girsanov change of measure. When used as a path measure, the Ito-Girsanov expression generates an ensemble of double-ended paths that are unphysical. We expose the underlying reasons why this continuous-time limit does not, and cannot, generate a thermodynamic ensemble of paths. Furthermore, we show that the concept of the Most Probable Path and the Thermodynamic action are incompatible with such measures for discrete or continuous time diffusion processes.

cond-mat.stat-mech↗