StatisticalMechanics.Ensemble

This module provides generic functionality to deal with ensembles in statistical mechanics.

Documentation

class StateProbability a where

The state probability functions provide conversion from some types a into non-normalized probabilities. For "real" applications, using the logProbability function is preferred. This functions allows for easy abstraction when types a are given as fractions of some actual value (say: deka-cal), or are discretized.

The returned values are not normalized, because we do not now the total evidence Z until integration over all states has happened -- which is not feasible in a number of problems.

TODO replace () with temperature and results with non-normalized P or LogP, depending. At some point we want to have type-level physical quantities, hence the need for the second type.

Methods

stateProbability

Arguments

:: Double

this is k*T

-> a

the energy (or discretized energy)

-> Probability NotNormalized Double

probability of being in state a, but only proportional up to 1/Z.

Given a temperature and a state "energy", return the corresponding non-normalized probability.

stateLogProbability

Arguments

:: Double

this is 1/(k * T)

-> a

the energy (or discretized energy)

-> Log (Probability NotNormalized Double)

resulting probability

Instances

StateProbability Double

Defined in StatisticalMechanics.Ensemble

Methods

stateProbability :: Double -> Double -> Probability 'NotNormalized Double

stateLogProbability :: Double -> Double -> Log (Probability 'NotNormalized Double)