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\title{Problem 3.15}
\subtitle{Entropy maximum and temperature}
\author{\begin{telugu}హృదయ్ దీపక్ మల్లుభొట్ల\end{telugu}}
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	Explain in words why, for two weakly coupled systems
	\begin{equation}
		\rho(E_1) = \flatfrac{\Omega_1(E_1) \Omega_2(E - E_1)}{\Omega(E)}
	\end{equation}
	is intuitive for a system where all states of energy $E$ have equal probability density.
	Using $S = \kb \log(\Omega)$, show in one step that maximising the probability of $E_1$ makes the two temperatures $\frac{1}{T} = \pdv{S}{E}$ the same, and hence that maximising $\rho(E_1)$ maximises the total entropy.

	\section{Solution} \label{sec:solution}

	Basically just a probability calculation of independent stuff, so it's intuitive.
	
	Derivative is easy enough.

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