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modified: ../../env/.aspell.en.pws

modified:   ../METADATA
modified:   appendixchapters.tex
renamed:    ../blogit/relStatMechExplorationFig1.png -> figures/relStatMechExplorationFig1.png
renamed:    ../blogit/relStatMechExplorationFig2.png -> figures/relStatMechExplorationFig2.png
renamed:    ../blogit/relStatMechExploration.tex -> relStatMechExploration.tex
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1 parent 668f24c commit b7c229af5ce984368190eaf5b66a39a698f267d0 @peeterjoot committed Mar 23, 2013
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22 env/.aspell.en.pws
@@ -7,8 +7,8 @@ confocal
ParametericPlot
Indistinguishability
Exponentiating
-Fick's
Ficks
+Fick's
cgs
phasor
linestyle
@@ -87,8 +87,8 @@ Eikonal
Goldstein's
GPS
colinear
-Hmm
hoc
+Hmm
Peeter's
Benard
ijk
@@ -160,8 +160,8 @@ Hestenes's
parametrizations
imaginaries
reparametrize
-nlm
n'l'm
+nlm
PDE
Lut
quantized
@@ -188,8 +188,8 @@ arctan
entropic
invertible
pion
-OuterMorphism
outermorphism
+OuterMorphism
QFT
rescaling
spinors
@@ -246,8 +246,8 @@ Denker
overdot
Srednicki
perturbative
-SVD
microstate
+SVD
graphene
uniaxial
Sackur
@@ -310,8 +310,8 @@ df
LIGO
spacetime
dH
-dj
BT
+dj
Routhian
dk
dL
@@ -339,9 +339,9 @@ Prandtl
ia
isync
inferometer
+eV
ib
iB
-eV
orthonormalization
ic
ie
@@ -355,16 +355,16 @@ variates
im
Dekker's
ji
-KE
jj
+KE
elastostatics
amino
-jk
ip
+jk
indices
kj
-kk
iu
+kk
mc
mE
iz
@@ -377,8 +377,8 @@ Strang's
xyz
mk
resistive
-kx
mn
+kx
Eulerian
anticommutes
n'l
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9 notes/METADATA
@@ -3053,6 +3053,14 @@ my @phy452 =
URL => 'http://sites.google.com/site/peeterjoot2/math2013/kittelCh3Zipper.pdf',
WHAT => qq()
}
+,{
+ SOURCE => 'relStatMechExploration',
+ TITLE => qq(Relativisitic generalization of statistical mechanics),
+ DATE => 'March 23, 2013',
+ REF => 'relStatMechExploration',
+ URL => 'http://sites.google.com/site/peeterjoot2/math2013/relStatMechExploration.pdf',
+ WHAT => qq()
+}
) ; # @phy452
my @phy454 =
@@ -5249,3 +5257,4 @@ sub printHistory
}
}
+
View
2 notes/phy452/appendixchapters.tex
@@ -12,5 +12,7 @@ \chapter{Addition of two one half spins}
\input{spinOneHalfAdditionReview.tex}
\chapter{Langevin small approximation}
\input{langevinSmallApprox.tex}
+\chapter{Relativisitic generalization of statistical mechanics}
+ \input{relStatMechExploration.tex}
\chapter{Mathematica notebooks}
\input{mathematica.tex}
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0 notes/blogit/relStatMechExplorationFig1.png → ...52/figures/relStatMechExplorationFig1.png
File renamed without changes
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0 notes/blogit/relStatMechExplorationFig2.png → ...52/figures/relStatMechExplorationFig2.png
File renamed without changes
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35 notes/blogit/relStatMechExploration.tex → notes/phy452/relStatMechExploration.tex
@@ -2,26 +2,25 @@
% Copyright © 2013 Peeter Joot. All Rights Reserved.
% Licenced as described in the file LICENSE under the root directory of this GIT repository.
%
-\input{../blogpost.tex}
-\renewcommand{\basename}{relStatMechExploration}
-\renewcommand{\dirname}{notes/phy452/}
-\newcommand{\keywords}{Statistical mechanics, PHY452H1S, special relativity, four vector, Boltzmann factor, energy, momentum, four momentum, microstate, equilibrium, temperature, reservoir, subsystem, Pathria}
-
-\input{../peeter_prologue_print2.tex}
-
-\beginArtNoToc
-
-\generatetitle{Relativistic generalization of statistical mechanics}
-%\chapter{Relativisitic generalization of statistical mechanics}
+%\input{../blogpost.tex}
+%\renewcommand{\basename}{relStatMechExploration}
+%\renewcommand{\dirname}{notes/phy452/}
+%\newcommand{\keywords}{Statistical mechanics, PHY452H1S, special relativity, four vector, Boltzmann factor, energy, momentum, four momentum, microstate, equilibrium, temperature, reservoir, subsystem, Pathria}
+%
+%\input{../peeter_prologue_print2.tex}
+%
+%\beginArtNoToc
+%
+%\generatetitle{Relativistic generalization of statistical mechanics}
\label{chap:relStatMechExploration}
-\section{Motivation}
+\paragraph{Motivation}
I was wondering how to generalize the arguments of \citep{pathriastatistical} to relativistic systems. Here's a bit of blundering through the non-relativistic arguments of that text, tweaking them slightly.
I'm sure this has all been done before, but was a useful exercise to understand the non-relativistic arguments of Pathria better.
-\section{Generalizing from energy to four momentum}
+\paragraph{Generalizing from energy to four momentum}
Generalizing the arguments of \S 1.1.
@@ -53,7 +52,7 @@ \section{Generalizing from energy to four momentum}
where $\Bv_i$ is the velocity of the particle in that observer frame.
-\section{Generalizing the number if microstates, and notion of thermodynamic equilibrium}
+\paragraph{Generalizing the number if microstates, and notion of thermodynamic equilibrium}
Generalizing the arguments of \S 1.2.
@@ -71,7 +70,7 @@ \section{Generalizing the number if microstates, and notion of thermodynamic equ
where $P = \lr{E/c, \BP}$ is the total four momentum of the system. If we have a system subdivided into to two systems in contact as in \cref{fig:relStatMechExploration:relStatMechExplorationFig1}, where the two systems have total four momentum $P_1$ and $P_2$ respectively.
-\imageFigure{relStatMechExplorationFig1}{Two physical systems in thermal contact}{fig:relStatMechExploration:relStatMechExplorationFig1}{0.2}
+\imageFigure{figures/relStatMechExplorationFig1}{Two physical systems in thermal contact}{fig:relStatMechExploration:relStatMechExplorationFig1}{0.2}
In the text the total energy of both systems was written
@@ -132,7 +131,7 @@ \section{Generalizing the number if microstates, and notion of thermodynamic equ
As in the text, let's consider a very large heat reservoir $A'$ and a subsystem $A$ as in \cref{fig:relStatMechExploration:relStatMechExplorationFig2} that has come to a state of mutual equilibrium. This likely needs to be defined as a state in which the four vector $\beta_\mu$ is common, as opposed to just $\beta_0$ the temperature field being common.
-\imageFigure{relStatMechExplorationFig2}{A system $A$ immersed in heat reservoir $A'$}{fig:relStatMechExploration:relStatMechExplorationFig2}{0.2}
+\imageFigure{figures/relStatMechExplorationFig2}{A system $A$ immersed in heat reservoir $A'$}{fig:relStatMechExploration:relStatMechExplorationFig2}{0.2}
If the four momentum of the heat reservoir is $P_r'$ with $P_r$ for the subsystem, and
@@ -179,8 +178,8 @@ \section{Generalizing the number if microstates, and notion of thermodynamic equ
}.
\end{equation}
-\section{Next steps}
+\paragraph{Next steps}
This looks consistent with the outline provided in \href{http://physics.stackexchange.com/a/4950/3621}{http://physics.stackexchange.com/a/4950/3621} by Lubos to the stackexchange ``is there a relativistic quantum thermodynamics'' question. I'm sure it wouldn't be too hard to find references that explore this, as well as explain why non-relativistic stat mech can be used for photon problems. Further exploration of this should wait until after the studies for this course are done.
-\EndArticle
+%\EndArticle

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