Changes between Version 4 and Version 5 of u/JCFeb0713

Timestamp:

02/07/13 15:47:52 (12 years ago)

Author:

Jonathan

Comment:

—

u/JCFeb0713

@@ -23 +23 @@
 [[Image(JC1.png, width=600)]]
 
-Taking the entropy
-
-[[latex(S(E,x)=k_B \log \Omega(E,x))]]
-
-and the canonical partition function
+From the canonical partition function
 
 [[latex(Z(T,F)=\int dE dx \Omega(E,x) \exp{-\left(E+Fx)/k_BT\right)})]]
 
-[[latex(\frac{1}{T}=\frac{\partial S}{\partial E})]]
+we can derive 
 
-[[latex(\frac{F}{T}=\frac{\partial S}{\partial x})]]
+[[latex(\frac{F}{T}=\frac{\partial S}{\partial x} = -C x)]]
+
+[[latex(F = -C T x)]]
+
+=== Black hole entropy ===
+
+Proportional to surface area of even horizon
+
+[[latex(S_{BH}=\frac{kA}{4l_p^2})]]
+
+where
+
+[[latex(l_p=\sqrt{G\hbar/c^3})]]
+
+(BH does not stand for 'black hole', but for Bekenstein-Hawking)
+
+Entropy is stored on surface ' holographic principle'
+
+Black holes also have a Hawking Temperature
+
+[[latex(T_H=\frac{\hbar c^3}{8\piGMk_B})]]
+
+If we assume that the Bekenstein-Hawking entropy times the Hawking temperature must equal the work done by gravity, then we have
+
+[[latex(F=T_H\frac{\partial S_{BH}}{\partial x})]]
 
 
-[[latex(T=\frac{\hbar k}{2\pi})]]
-[[latex(S=\frac{4A}{G})]]
+What about 
+
  * Space has one emergent holographic direction.  
  * There is a change of entropy in the emergent direction
@@ -45 +65 @@
 
 
-