- #1
ianhoolihan
- 145
- 0
Hi all,
Firstly, I'm not sure where to post this thread, but I'm hoping here is the right place. My questions developed through reading Verlinde's paper on entropic gravity:
http://arxiv.org/abs/1001.0785"
However my questions are with the introductory thermodynamic ideas he presents on entropy with polymers.
Firstly, I was wondering how the partition function (2.2) was arrived at? Specifically, from all that I've read on the internet, I don't see where the omega factor comes in?
Secondly, how are the relations (2.3) derived from the 'saddle point equations'? From what I gather, solving these saddle-point equations (2.3) gives the saddle points of the function [tex]\Omega{}e^{-(E+Fx)/kt}[/tex]. I should then be able to evaluate the integral Z. But why do I want to do that? What is the signficance of these saddle point equations? In terms of entropy?
Thirdly, how does (2.4) imply these saddle equations? I can see how if one defines [tex]\frac{dS}{dE}=\frac{1}{T}[/tex], but he seems to indicate that this is not needed?
Anyway, any help would be much appreciated = )
Cheers
Firstly, I'm not sure where to post this thread, but I'm hoping here is the right place. My questions developed through reading Verlinde's paper on entropic gravity:
http://arxiv.org/abs/1001.0785"
However my questions are with the introductory thermodynamic ideas he presents on entropy with polymers.
Firstly, I was wondering how the partition function (2.2) was arrived at? Specifically, from all that I've read on the internet, I don't see where the omega factor comes in?
Secondly, how are the relations (2.3) derived from the 'saddle point equations'? From what I gather, solving these saddle-point equations (2.3) gives the saddle points of the function [tex]\Omega{}e^{-(E+Fx)/kt}[/tex]. I should then be able to evaluate the integral Z. But why do I want to do that? What is the signficance of these saddle point equations? In terms of entropy?
Thirdly, how does (2.4) imply these saddle equations? I can see how if one defines [tex]\frac{dS}{dE}=\frac{1}{T}[/tex], but he seems to indicate that this is not needed?
Anyway, any help would be much appreciated = )
Cheers
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