Long Range Correlations in a Closed System, With Applications to Nonuniform Fluids Classic Reprint

Local equilibrium and how slow changes in density and temperature shape fluid behavior

In this work, Lebowitz explores how a one-component or multi-component fluid can be described as locally at equilibrium even when its density, temperature, and flow vary slowly in space. The book shows how local variables determine distribution functions and how particle correlations adapt to gentle inhomogeneity.

The discussion builds a framework where each small region behaves like a fluid with its own temperature, velocity, and density, yet remains connected to neighboring regions. It explains how two- and many-body distributions relate to local conditions and how a local chemical potential emerges from gradual changes in the system. The treatment covers classical and quantum cases, highlighting when local approximations hold and where they fail.

Key topics include the structure of local distribution functions, the role of correlation (or Ursell) functions, and how gradients in intensive variables shape statistical properties. The text also applies these ideas to mixtures, light scattering, and how intrinsic correlations extend beyond simple one-body pictures. Readers will see how nonuniform fluids can be analyzed without losing the clarity of uniform-system results.

• How slow spatial variations in density, temperature, and velocity affect local distributions
• Why a slowly varying density can be treated as changes in local chemical potential
• How two- and multi-particle correlations adapt in nonuniform fluids
• Applications to fluid mixtures and scattering phenomena

Ideal for readers of statistical mechanics, theoretical fluid science, and applications to nonuniform fluids.