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Ensembles

statisticalphysics.leima.is · 6,031 words · saved by 1 readers

In statistical mechanics, only partial information of the system can be observed. From a macroscopic point of view, thermodynamic observables do not tell us about all the information of the microstates. The contimiuum in the phase space, aka, the phase space distributions, is used to represent the internal stuctures of the system. For equlibrium physics, the probability distribution of the microstates ρ({ p i },{ q i }) 𝜌 ( { 𝑝 𝑖 } , { 𝑞 𝑖 } ) may be used to calculate the macroscopic observables 𝒪 𝑂 , i.e., ⟨𝒪⟩(t)=∫𝒪({ p i },{ q i })ρ({ p i },{ q i })dΩ ⟨ 𝑂 ⟩ ( 𝑡 ) = ∫ 𝑂 ( { 𝑝 𝑖 } , { 𝑞 𝑖 } ) 𝜌 ( { 𝑝 𝑖 } , { 𝑞 𝑖 } ) 𝑑 Ω . The question is how to obtain the probability density ρ({ p i },{ q i }) 𝜌 ( { 𝑝 𝑖 } , { 𝑞 𝑖 } ) , i.e., the probability density distribution of phases space points. In the language of statistics, we either invent a know-all theory which involves the whole population of microscopic states, or a good sampling method to sample some repres

Ensembles — Statistical Physics Notes Statistical Physics Chapters Vocabulary and Program Functions Stability Analysis Integrals Transforms Green’s Function Computations Thermodynamics Summary Topics on Thermodynamics Equilibrium Statistical Mechanics Equilibrium Statistical Mechanics Summary Basics of Statistical Mechanics \(\Gamma\) Space and \(\mu\) Space Macroscopic States and Microscropic State Most Probable Distribution Harmonic Oscillator and Density of States Gibbs Mixing Paradox Observables in Statistical Physics Debye Model Phase Transitions Gas Revisited Ising Model A More Sys

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