Statistical mechanics

Lore & Background

The founding of statistical mechanics is generally credited to three physicists: Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates; James Clerk Maxwell, who developed models of probability distribution of such states; and Josiah Willard Gibbs, who coined the name of the field in 1884. In 1738, Daniel Bernoulli published Hydrodynamica, laying the basis for the kinetic theory of gases, arguing that gases consist of molecules moving in all directions, that their impact on a surface causes gas pressure, and that heat is the kinetic energy of their motion. In 1859, after reading a paper on diffusion by Rudolf Clausius, Maxwell formulated the Maxwell distribution of molecular velocities, the first-ever statistical law in physics, and gave the first mechanical argument that molecular collisions entail an equalization of temperatures and a tendency towards equilibrium. In 1864, Boltzmann, then a young student in Vienna, encountered Maxwell's paper and spent much of his life developing the subject further. Boltzmann introduced the concept of an equilibrium statistical ensemble and investigated non-equilibrium statistical mechanics with his H-theorem. Gibbs published Elementary Principles in Statistical Mechanics in 1902, formalizing statistical mechanics as a fully general approach for all mechanical systems, initially derived in classical mechanics but adaptable to quantum mechanics.

Reader's Guide

Statistical mechanics fills the disconnect between the laws of mechanics—which describe the complete state of a system and its equation of motion—and the practical experience of incomplete knowledge at the human scale. It introduces the statistical ensemble, a large collection of virtual, independent copies of the system in various states, representing a probability distribution over all possible states. In classical statistical mechanics, the ensemble is a distribution over phase points; in quantum statistical mechanics, it is a distribution over pure states summarized as a density matrix. The ensemble can be interpreted as epistemic probability (representing possible states of a single system) or empirical probability (states of repeated experiments). Equilibrium ensembles do not evolve over time and are the focus of statistical thermodynamics, which derives classical thermodynamics from microscopic properties. Non-equilibrium statistical mechanics addresses ensembles that change over time or non-isolated systems, studying irreversible processes such as chemical reactions and flows of particles and heat; the fluctuation–dissipation theorem is a basic result from applying it to steady state current flow. The term 'statistical mechanics' was coined by Gibbs in 1884, based on Maxwell's 1871 use of 'statistical method of calculation'.

Did You Know?

• The term 'statistical mechanics' was coined by Josiah Willard Gibbs in 1884.
• James Clerk Maxwell formulated the first-ever statistical law in physics in 1859: the Maxwell distribution of molecular velocities.
• Ludwig Boltzmann introduced the concept of an equilibrium statistical ensemble and investigated non-equilibrium statistical mechanics with his H-theorem.
• Daniel Bernoulli's 1738 work Hydrodynamica laid the basis for the kinetic theory of gases.