Coarse Graining: What Does It Mean?

[touqra]

I keep reading papers with the term "coarse graining". What does it mean?
An example of a paper having this term is hep-th/0504037.

 

[marcus]

I keep reading papers with the term "coarse graining". What does it mean?
An example of a paper having this term is hep-th/0504037.

http://arxiv.org/abs/hep-th/0504037

I hope you get several explanations from different people.

My understanding is that (although it can have precise technical meanings depending on context) the term expresses a GENERAL IDEA and the root analogy is with image processing.

in photography you can have fine grain film (small pixels) and coarse grain film (large pixels)
and you can take a finegrain image and progressively coarsen the grain

until finally it might look like one of those pictures made of greytone squares on a graphpaper grid. it can be so coarsegrained you can't recognize it except you hold it out some distance

As if you lay graphpaper tracing paper over something and in each square you average the greytone so it is uniform within that square
you end up with a crude matrix of numbers which tell the greyscale in each pixel

IN COARSEGRAINING SOME OF THE MICROSCOPIC INFORMATION IS ELIMINATED or averaged out so that you end up with MUCH FEWER NUMBERS DESCRIBING whatever it is.

So the ultimate coarsegraining in THERMODYNAMICS where you just know really gross degrees of freedom like "pressure" "temperature" "volume"
and you CANT SEE the antheap of activity inside the gas with all the molecules whizzing crazily around, all that microscopic information has been washed out or erased and summarized by 2 or 3 coarse variables.

And with a black hole the HORIZON does the coarsegraining for you because there may be millions of things happening inside related to gravitational collapse but you never see that, all you supposedly see is the area and temperature of the event horizon, and whatever diddly Hawking radiation is percolating out. it's very coarsegrain.

 

[R0man]

Coarse graining refers to a method used in physics, mathematics, and other fields to simplify complex systems by grouping together smaller components into larger entities. This is done in order to reduce the complexity of a system and make it more manageable for analysis or simulation.

In the context of the paper hep-th/0504037, which is about quantum field theory, coarse graining is used to describe the process of averaging over small scale quantum fluctuations to obtain a more simplified and effective description of the system at larger scales. This is particularly useful in cases where the small scale fluctuations are not relevant to the overall behavior of the system.

In general, coarse graining involves identifying the relevant variables or parameters that describe the system at a certain scale, while ignoring or averaging out the details at smaller scales. This allows for a more efficient and practical analysis of complex systems, while still capturing the essential features and behavior.

In summary, coarse graining is a powerful tool for simplifying and understanding complex systems, and it is commonly used in various fields of science and engineering.