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The study of large, complicated systems by means of statistics and probability theory, in order to extract average properties and to provide a connection between mechanics and thermodynamics.

2
votes
The relationship between the Laplace and Legendre transforms is through the method of steepest descent, which is usually exact in the thermodynamic limit (since the configuration space typically goes …
answered Sep 4 '15 by TotallyRhombus
2
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In the microcanonical ensemble, all states with a fixed energy are equally probable. In classical mechanics, this follows essentially from ergodic theory (non-linear systems tend not to have 'many' co …
answered Mar 9 '17 by TotallyRhombus
1
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A typical renormalization group flow can be thought of as a smooth vector field $\vec V(\mu)$ defined on parameter space. Starting with parameters $\vec\mu(\ell)$ at scale $\ell$, you obtain parameter …
answered Nov 1 '15 by TotallyRhombus
1
vote
In many situations in statistical mechanics, the configuration space that you sum over in your partition function is coarse-grained in a way that certain microscopic degrees of freedom are ignored. Th …
answered Jun 20 '15 by TotallyRhombus
4
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In general, the density of states can be computed as follows: Find eigenstates of the Hamiltonian, $\psi_{s}$, so that $H\psi_s=E_s\psi_s$ (except in special cases, this is usually the hardest part) …
answered Jun 29 '15 by TotallyRhombus
1
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The Hamiltonians $H_S$ and $H_R$ both implicitly depend on their respective volumes (or confining potential strength). To allow volume exchange between the two systems, you simply impose the constrain …
answered Jan 25 '16 by TotallyRhombus
1
vote
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The classical justification for the microcanonical ensemble relies on the fact that most many-body systems have just a 'small' (typically finite) number of conserved quantities (i.e. they violate ergo …
asked Mar 5 '17 by TotallyRhombus
7
votes
To determine the upper limit on chemical potential for a gas of $\mathcal N$ bosons, look at the form of the Bose distribution in the grand canonical ensemble with $\langle N \rangle = \mathcal N$. Wh …
answered Jan 16 '16 by TotallyRhombus
1
vote
The physical principle being invoked is the finite resolution of any experiment, independent of the value of $\hbar$, together with coupling between observable and microscopic degrees of freedom, i.e. …
answered May 17 '16 by TotallyRhombus