Thermodynamic limit

The limit in which a system’s particle number and volume grow without bound at fixed density. It provides a framework for describing bulk matter while removing finite-size effects.

Extensive and intensive properties: Extensive properties scale with system size, while intensive properties remain unchanged when a system is divided. Fixed density keeps an intensive property constant as particle number and volume grow.
Phase transition: A change between distinct macroscopic states of matter as an external condition varies. Sharp phase transitions generally emerge only when system size becomes infinite.
Finite-size effect: A deviation in a system’s behavior caused by its finite dimensions or particle number. These are the corrections the thermodynamic limit is designed to eliminate.
Kac scaling: A rescaling of long-range interaction strength with system size used to obtain an extensive thermodynamic limit. It modifies interaction strengths when the ordinary fixed-coupling limit is ill behaved.
Finite-size scaling: A method for analyzing how observables vary with system size to infer their behavior in the infinite-size limit. It quantifies how finite systems approach thermodynamic-limit behavior.
Spontaneous symmetry breaking: A state in which a system’s realized configuration lacks a symmetry of its governing laws. A finite system can preserve symmetry while the thermodynamic limit permits distinct symmetry-broken states.
Canonical ensemble: A statistical ensemble describing systems with fixed particle number, volume, and temperature. It defines finite-volume quantities whose large-system behavior can be studied.
Long-range interaction: An interaction whose strength decays slowly enough with distance to couple distant parts of a system significantly. Such interactions challenge the usual assumptions behind thermodynamic-limit arguments.
Boundary conditions: Rules specifying how a physical system behaves at its spatial boundaries. Boundary choices affect finite systems, but their influence often vanishes in the bulk limit.
Equation of state: A relation among thermodynamic variables that characterizes the equilibrium state of a material. Bulk equations of state describe quantities after finite-size corrections become negligible.

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