Difference between revisions of "Essential Reading"

From RedwoodCenter
Jump to navigationJump to search
 
 
(2 intermediate revisions by the same user not shown)
Line 6: Line 6:
  
 
2. Connect these to machine learning of time series via objectives like Minimum Conditional Entropy Production.
 
2. Connect these to machine learning of time series via objectives like Minimum Conditional Entropy Production.
 +
Understand the relation of new work-based objectives to classical unsupervised learning objectives like
 +
maximum likelihood.
 +
  
 
PAPERS:
 
PAPERS:
Line 18: Line 21:
  
 
Crooks G.E. 2007. Beyond Boltzmann-Gibbs statistics: Maximum entropy hyper-ensembles out of equilibrium
 
Crooks G.E. 2007. Beyond Boltzmann-Gibbs statistics: Maximum entropy hyper-ensembles out of equilibrium
 +
  
 
The following 3 papers are very insightful and contain some of the most advanced ideas
 
The following 3 papers are very insightful and contain some of the most advanced ideas
Line 26: Line 30:
  
 
Parrondo J.M.R., Van den Broeck \& Kawai R. 2009. Entropy production and the arrow of time
 
Parrondo J.M.R., Van den Broeck \& Kawai R. 2009. Entropy production and the arrow of time
 +
  
 
Mae's papers are really difficult and confusing but they seem to be the most advanced work.
 
Mae's papers are really difficult and confusing but they seem to be the most advanced work.
Line 35: Line 40:
  
 
Maes C. 2001. Statistical mechanics of entropy production: Gibbsian hypothesis and local fluctuations
 
Maes C. 2001. Statistical mechanics of entropy production: Gibbsian hypothesis and local fluctuations
 +
  
 
Kurchan J. 2005. Non-equilibrium work relations
 
Kurchan J. 2005. Non-equilibrium work relations

Latest revision as of 00:28, 18 July 2009

GOALS:

1. Understand the relations between entropy production, free energy changes and work done in the non-equilibrium regime of Markov processes and deterministic Hamiltonian dynamics. ie: understand all the different Fluctuation Theorems.

2. Connect these to machine learning of time series via objectives like Minimum Conditional Entropy Production. Understand the relation of new work-based objectives to classical unsupervised learning objectives like maximum likelihood.


PAPERS:

These are the most important papers from Crooks. His thesis goes through the theorems for Markov chains thoroughly. You will find it on his webpage www.threeplusone.com

Crooks G.E. 1999. Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences

Crooks G.E. 1999. Path ensemble averages in systems driven far from equilibrium.

Crooks G.E. 2007. Beyond Boltzmann-Gibbs statistics: Maximum entropy hyper-ensembles out of equilibrium


The following 3 papers are very insightful and contain some of the most advanced ideas

Gomez-Martin A., Parrondo J.M.R. \& Van den Broeck. 2008. The "footprints" of irreversibilty

Kawai R., Parrondo J.M.R. \& Van den Broeck. 2007. Dissipation: the phase-space perspective

Parrondo J.M.R., Van den Broeck \& Kawai R. 2009. Entropy production and the arrow of time


Mae's papers are really difficult and confusing but they seem to be the most advanced work. This one contains the path ensemble maths for markov chains.

Maes C. \& Netocny 2002. Time-reversal and entropy

This one you should read section 4 on Entropy Production and maybe sections 1 and 2 for background

Maes C. 2001. Statistical mechanics of entropy production: Gibbsian hypothesis and local fluctuations


Kurchan J. 2005. Non-equilibrium work relations

This is a useful short review of foundations. Not deep, but a good starting point if you're confused.

Karevski D. 2007. Foundations of statistical mechanics: in and out of equilibrium