Refine
Year of publication
Document Type
- Article (211)
- ZIB-Report (70)
- In Proceedings (23)
- In Collection (9)
- Book chapter (7)
- Book (2)
- Doctoral Thesis (2)
- Other (2)
- Poster (2)
- Habilitation (1)
Is part of the Bibliography
- no (331)
Keywords
- metastability (8)
- cycle decomposition (3)
- rare events (3)
- reaction coordinate (3)
- Bayesian inference (2)
- Clustering (2)
- DS-MLE (2)
- EM algorithm (2)
- Jeffreys prior (2)
- MPLE (2)
Institute
- Numerical Mathematics (151)
- Modeling and Simulation of Complex Processes (57)
- ZIB Allgemein (29)
- Visual and Data-centric Computing (23)
- Computational Systems Biology (18)
- Computational Molecular Design (13)
- Visual Data Analysis (13)
- Mathematics for Life and Materials Science (5)
- Bioinformatics in Medicine (3)
- AI in Society, Science, and Technology (1)
Linear response theory and optimal control for a molecular system under nonequilibrium conditions
(2013)
In this paper, we propose a straightforward generalization of linear
response theory to systems in nonequilibrium that are subject to
nonequilibrium driving. We briefly revisit the standard linear response
result for equilibrium systems, where we consider Langevin dynamics
as a special case, and then give an alternative derivation using a
change-of-measure argument that does not rely on any stationarity or
reversibility assumption. This procedure moreover easily enables us
to calculate the second order correction to the linear response formula
(which may or may not be useful in practice). Furthermore, we outline
how the novel nonequilibirum linear response formula can be used to
compute optimal controls of molecular systems for cases in which one
wants to steer the system to maximize a certain target expectation
value. We illustrate our approach with simple numerical examples.
In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality.