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Thermal and Statistical Physics > Autumn Statistical > Flashcards

Autumn Statistical Flashcards

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1
Q

How many ways are there of choosing n from N distinct objects?

A
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2
Q

What is C(N,n)?

A

The number of ways to choose n from N distinct objects

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3
Q

What is a macrostate?

A

a thermodynamic state of a system defined by macroscopic functions of state e.g. temp, pressure etc

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4
Q

What is a microstate?

A

A quantum state of our system, specifying all relevant details about all particles e.g. position, velocity, spin

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5
Q

What does PEAPP stand for?

A

Principle of Equal A Priori Probability

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6
Q

What is the PEAPP?

A

When an isolated system reaches equilibrium, all microstates accessible to it are equally probable

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7
Q

How is entropy defined statistically?

A

S = kBlnP where P is probability

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8
Q

How is ΔS defined statistically? (two ways to write constants)

A

ΔS = NkBlnP1/P2 or = nRln2#P1/P2

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9
Q

What is S=kBln2 also known as?

A

Boltzmann’s entropy process

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10
Q

How is S written in terms of W (statistical) what is W?

A

(entropy of a macrostate) S = kblnW
where W is number of microstates available for that macrostate

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11
Q

If a macrostate has a larger W, it is…?

A

More probable

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12
Q

What is W?

A

Number of microstates in a macrostate

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13
Q

How are P and W related?

A

Proportional, probability is proportional to number of microstates

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14
Q

What W should we seek to find equilibrium state? Why?

A

The maximum, because the equilibrium state is the most probable.

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15
Q

What is the equation for statistical temperature?

A
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16
Q

What is Stirling’s approximation?

A
17
Q

How is Stirling’s approximation derived?

A
18
Q

What is the law of large numbers?

A
19
Q

What does the Law of large numbers effectively mean (qualitatively)?

A

Uncertainties/fluctuations are essentially supressed by large numbers

20
Q

What is the central limit theorem?

A

Sum of independent variables tends to a normal distribution even if the original variables are not normally distributed

21
Q

Define an ensemble.

A

a collection of identical systems, whose statistical fluctuations are cancelled out upon averaging

22
Q

What is the micro-canonical ensemble?

A

Systems with fixed number of particles N, total energy E, and volume V

23
Q

What is the Canonical ensemble?

A

Systems with fixed V, N and T as they are in contact with a heat bath

24
Q

By the Boltzmann distribution, what is the probability of finding a system in a particular microstate of the canonical ensemble is?

A
25
Q

What are the ‘differences between PEAPP and Boltzmann?

A

PEAPP: equal distribution, for the micro-canonical ensemble, counts all microstates including the heat bath

Boltzmann: exp distribution, for the canonical ensemble, counts probability of the system only not the heat bath

26
Q

What is Gibb’s entropy? Why might it be used over Boltzmann’s?

A

Gibbs applies to both canonical and micro-canonical ensembles so is more general

27
Q

What is Shannon’s theorem?

A

the equation for (when maximised) the most likely distribution of a set of mutually exclusive probabilities pi

28
Q

For a two level system with possible energies 0 or epsilon, how are probabilities of the atom being in either level found using the Boltzmann distribution?

A
29
Q

For the two level system, how can the number of particles on a level be found using probability from the Boltzmann distribution?

A
30
Q

What ‘type’ of ensemble does Boltzmann distribution use?

A

Canonical ensemble

31
Q

For the two level system, we calculate probability of energies using the Boltzmann system so we use the __________ formula for the entropy.

A

Gibbs

32
Q

How does Z relate to F?

A
33
Q
A

Thermal and Statistical Physics (3 decks)

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