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Entropy of a continuous system 
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#1
Feb2013, 06:55 PM

P: 282

How could the entropy of a continuous system, like the electromagnetic field, be defined? Obviously you can't use something like the log of the phase space volume, but I can't think of anything that would work.



#2
Feb2013, 07:10 PM

Sci Advisor
P: 5,523

If you can assign a temperature (which you can for blackbody radiation), you can define the entropy:
http://128.113.2.9/dept/phys/courses...BodyThermo.pdf 


#3
Feb2013, 11:09 PM

PF Gold
P: 1,165




#4
Feb2013, 11:33 PM

P: 1,066

Entropy of a continuous system
What's wrong with phase space volume? You can still write the Hamiltonian for a continuous system  it would just be a field theory now.



#5
Feb2113, 05:47 PM

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#6
Feb2113, 08:27 PM

Sci Advisor
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#7
Feb2213, 12:46 AM

P: 789

For example, for a simple fluid, the fundamental law says [itex]dU=T dSP dV+\mu dN[/itex] where U is internal energy, T is temperature, S is entropy, P pressure, V volume, [itex]\mu[/itex] chemical potential, and N the number of particles. So it follows that [itex]dS=(1/T)dU+(P/T)dV(\mu/T)dN[/itex] and in terms of densities: [tex]\frac{\partial s}{\partial t}=\frac{1}{T}\frac{\partial u}{\partial t}\frac{\mu}{T}\frac{\partial n}{\partial t}[/tex] where u is internal energy density and n is particle density. And so forth. In statistical mechanics terms, you are considering each infinitesimal volume element to be an open equilibrated system. To find the total entropy, integrate the entropy density over the total volume. 


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