Blundell Thermal Physics · Problem 34.1

Non-equilibrium thermodynamics

Physics — Statistical Mechanics · fluctuations-helmholtz-free-energy

Problem

If a system is held at fixed

T

N

, and

V

, show that the fluctuations in a variable

x

are governed by the probability function

p(x) \propto \mathrm{e}^{-F(x)/k_\mathrm{B}T},\tag{34.64}

where

F(x)

is the Helmholtz function.