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4

You have to distinguish between "different states" and "number of states" - or, in the words of @Numrok, between "macrostates" and "microstates". The fundamental theorem refers to "accessible micro states". If I have three white balls and two buckets to put them in, I could put two balls in one and one in the other (that is a macro state); there are in fact ...


3

The probability for one compartment being empty is actually the probability that at least one compartment is empty. Let's call it $\Pi^{(1)}$, $$ \Pi^{(1)} = \frac{(p-1)^N}{p^N} $$ When you write the probability for any of the compartments to be empty as $$ \Pi = \sum_{j=1}^{p}{\Pi^{(1)}} = p\frac{(p-1)^N}{p^N} $$ you are overcounting. Longer argument: ...


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The uses of this two theories are completely different. Statistical Mechanics is used to see how by modelling the behavior of microscopic constituents you can predict the macroscopic phenomenas that you observe. On the other hand Many Body Theory uses first principle techniques to see what happens microscopically when you have large no of particles in your ...


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I see at least 3 reasons. It is only in this limit that macroscopic observables become deterministic. It is only in this limit that one has equivalence of the different statistical ensembles. It is only in this limit that one has sharp phase transitions (genuine singularities of thermodynamic potentials). (The first two properties may fail to hold even ...


2

At equilibrium, the system would be in that macrostate which would have the maximum multiplicity or the largest number of microstates; that would correspond to gas totally dispersed over the whole volume $V\;.$ This is wrong, and based on a misunderstanding of terminology. You have microstates, and macrostates. A macrostate assigns a probability to each ...


1

You say: We shouldn't care about how we reached that equilibrium In fact the entire point of the example is that we do. I shall try to explain why. Jaynes and Gull both work in the framework of Bayesian inference (I can recommend the introductory text: http://www.amazon.co.uk/Data-Analysis-A-Bayesian-Tutorial/dp/0198568320. The title may seem ...


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Assume each atom can be in only two states, n = 1 and n = 2, where its energy is respectively E1 and E2. In a gas, you have many atoms. At any given time, some of them are in state n = 1 and the rest are in state n = 2. The number of atoms in a state n is the "population of the state n ".


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In nuclear and particle physics, the primary data of interest are scattering cross sections. In these data, the structure of the particle(s) of interest shows up through various "resonances" in your data (i.e. big spikes in the data set). These resonances correspond to states of the system of particle(s) (e.g. nucleus, proton, etc.) of interest. The width of ...


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A CFT is still a QFT, and the way to put it at finite temperature is standard for any quantum system - you take your Hamiltonian $H$ and compute $Z=\mathrm{tr}\,e^{-\beta H}$, where the trace is over the Hilbert space of states living on $\mathbb{R}^{d-1}$ if your CFT is in $d$ dimensions. The thermal correlators are computed in a similar way, ...



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