Blundell Thermal Physics · Problem 33.1

Brownian motion and fluctuations

Physics — Statistical Mechanics · fluctuations-gibbs-function

Problem

If a system is held at fixed

T

N

and

p

, show that the fluctuations in a variable

x

are governed by the probability function

p(x) \propto \mathrm{e}^{-G(x)/k_\mathrm{B}T}, \tag{33.120}

where

G(x)

is the Gibbs function.