# Search Results

Results tagged with Search options user 27209
9 results

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.

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
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
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
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
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
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
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 …
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. …