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tags: stat mech
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# Dictionary

| Term | Description |
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| canonically conjugate variables | Pairs of variables mathematically defined in such a way that they become Fourier transform duals, which leads to an [uncertainty relation](https://en.wikipedia.org/wiki/Uncertainty_principle) between them. Conjugate variables are related by Noether's theorem, which states that if the laws of physics are invariant with respect to a change in one of the conjugate variables. <br> *Notation*: **p, q** denote the position, momentum pair |
| canonical ensemble | A very large number of identically prepared systems (real or imagined). The collection of possible states of a mechanical system in thermal equilibrium with a heat bath (or reservoir) at a fixed temperature T. See Stowe p 329 |
| canonical transformation | A change of canonical coordinates (q, p, t) → (Q, P, t) that preserves the form of Hamilton's equations (though not the Hamiltonian itself) |
| closed system | does not exchange energy with its environment/surroundings |
| conjugate momenta | $p_i(q,\dot q, t) = ∂L/∂\dot q^i$ |
| micro-canonical ensemble | Canonical ensemble with no interaction with outside systems (completely closed system) |
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| statistical ensemble | Collection of all accessible microstates of a system with associated probabilities |
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