Some general methods for deriving such equations are the master equation approach and an approach that relies upon coarse-graining the phase space of points representing the micro-states of the system into finite cells and assuming fixed transition probabilities from cell to cell (Markov assumption). ❋ Sklar, Lawrence (2009)
There is no such natural tendency, since no matter what coarse-graining you choose, there is an equal number of trajectories that decrease their entropy and trajectories that increase their entropy. ❋ Sean (2007)
How we do the coarse-graining to define which microstates are macroscopically equivalent is a classic question. ❋ Sean (2007)
(Where the entropy of a state is defined by its macroscopic equivalence class under the coarse-graining, which is a perfectly sensible thing to do.) ❋ Sean (2007)
Just a word on the coarse-graining Steve M. refers to above. ❋ Unknown (2007)
It is a large and manysided subject, connected with locality, relativity, coarse-graining and enthropy, and so on. ❋ Unknown (2006)
The foundations of statistical physics may today be characterized as a battlefield between a dozen or so different schools, each firmly dug into their own trenches, e.g., ergodic theory, coarse-graining ❋ Uffink, Jos (2004)
The primary aim of the proposed research is the development of state-of-the-art analytical and numerical methodologies for mode reduction, coarse-graining and multiscale analysis of ❋ Unknown (2010)
Nanomaterials: Design and Simulation explores the role that such advances have made toward a rational design of nanostructures and covers a variety of methods from ab initio electronic structure techniques, ab initio molecular dynamics, to classical molecular dynamics, also being complemented by coarse-graining and continuum methods. ❋ Unknown (2009)
Such a coarse-graining allows us to handel multi-million systems using OFDFT, which has not been possible to date. ❋ Ezio Bruno (2008)
Once this is done, then we will have access to all materials and all properties (structural, optical, electronic, magentic ...) (2) The standard quasi-continuum codes developed so far only handle the coarse-graining of the displacement field. ❋ Ezio Bruno (2008)
This was the main motivation for the development of QC-OFDFT, which is a seamless scheme for systematic and adaptive coarse-graining of OFDFT in a manner that enables consideration of multi-million atom systems at no significant loss of accuracy and without the introduction of spurious physics or assumptions. ❋ Ezio Bruno (2008)
We use the same physics everywhere in the domain (OFDFT) and use the power of coarse-graining to seamlessly transition from quantum mechanical length scale to continuum length scales. ❋ Ezio Bruno (2008)
But once you introduce coarse-graining, Thomas’ stability argument is absolutely correct. ❋ Sean (2007)
In the coarse-graining that everyone actually uses, our early universe had a very low entropy — much lower than it needed to have, by any known criterion — and that’s a fact that needs to be explained by cosmology. ❋ Sean (2007)
I would personally bet that our notion of the “most useful” coarse-graining can be derived as a consequence of the Hamiltonian of the world, but I haven’t been following the research along those lines. ❋ Sean (2007)
(iii) And, more importantly, it cant handle unstructured coarse-graining, which is the heart of our multi-scale scheme. ❋ Ezio Bruno (2008)
Complexity, coarse-graining, multiscale analysis and numerical methods "under the joint supervision of Dr S Kalliadasis, Department of Chemical Engineering and Chemical Technology and Dr GA Pavliotis, Department of Mathematics. ❋ Unknown (2010)
