# Workshops

## Fundamental Aspects of Deterministic Thermostats

July 27, 2009 to July 29, 2009
Location : CECAM-HQ-EPFL, Lausanne, Switzerland
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### Organisers

• Gregory Ezra (Cornell University, USA)
• Alessandro Sergi (University of Kwazulu-Natal, South Africa)
• Stephen Wiggins (University of Bristol, United Kingdom)

### Description

A fundamental problem in contemporary science is the necessity for qualitatively correct long-time simulations of large classical and mixed classical-quantum systems. Relevant areas of application include chemistry (biomolecules, liquids, materials), physics (lattice gauge theories, spin lattices) and biology (protein folding, membrane dynamics, molecular machines). The basic goal involves both <i>sampling</i> and <i>dynamics</i> for systems
that are members of ensembles other than standard microcanonical ensemble <i>(NVE)</i>, for example the canonical <i>(NVT)</i> or isothermal-isobaric <i>(NTP)</i> ensembles.
One approach, which forms the focus of the workshop, involves coupling the system of physical interest to additional thermostatting variables, whose role is to distribute the coordinates of the physical system over its phase space according to the desired distribution function.

Some important questions and topics for discussion at the workshop are:

<ul><li>Integration algorithms<ul><li>Symplectic <i>vs</i> non-symplectic (e.g., measure-preserving) algorithms in principle and in practice.
Origins of instabilities and possible solutions.</li><li>Trajectory reweighting schemes for improving accuracy of computed averages and distributions.</li><li>Large timesteps and Jarzynski-type free energy difference computations.</li><li>Development and implementation of generalized Poisson integrators for non-canonical and non-Hamiltonian systems.</li><li>Geometric integrators for rotational dynamics.</li><li>Geometric integration approaches to spin systems and Lie algebras: geometric demons''.</li><li>Constraints.</li><li>Mixed quantum-classical systems.</li><li>Electronic degrees of freedom.</li></ul></li>
<li>Hamiltonian & non-Hamiltonian thermostats<ul><li>Mappings between Hamiltonian and non-Hamiltonian systems.</li><li>Geometry of temperature: Configurational temperature and configurational thermostats.</li><li>Statistical mechanics of non-Hamiltonian systems:
Metric <i>vs</i> non-metric approaches.</li><li>Time-dependent thermostats. Shakers, etc.
</li></ul></li>
<li>Ergodicity and chaos in thermostatted systems: dynamical systems perspective<ul><li>Diagnostics of ergodicity and nonergodicity in thermostats.</li><li> Rigorous proofs of local integrability or non-integrability.</li><li>Application of concepts and methods of theory of multidimensional Hamiltonian systems.</li><li>Application of concepts and methods of reaction rate theory.
</li></ul></li>
<li>Deterministic <i>vs</i> stochastic thermostats
<ul><li>Combining stochastic and deterministic thermostatting mechanisms.</li></ul></li></ul>
<p style='text-align:justify'>
The aim of the workshop is to bring together experts on the various topics mentioned above, for discussion of fundamental theoretical and computationally relevant questions in thermostatted systems.
In particular, we believe the time is ripe for fruitful exchange of ideas between researchers knowledgeable about dynamical systems theory as applied to reaction dynamics and the community of molecular dynamics practitioners and experts on geometric integration algorithms. The invited talks and presentations will also serve as an introduction to the field for researchers new to the area.
</p><p style='text-align:justify'>
The overall goal is the establishment of a sound theoretical framework for rational, dynamics-based approaches to the design and assessment of deterministic thermostats.
</p>