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Theorem

H-Theorem

Mathematical Physics

The H-Theorem shows that a quantity called H, defined from the velocity distribution of particles in a dilute gas, decreases monotonically over time under the Boltzmann equation until the distribution reaches its equilibrium, Maxwell-Boltzmann form, at which point H stops changing. Proved by Ludwig Boltzmann, it was intended to give a mechanical derivation of the increase of entropy called for by the second law of thermodynamics, and it remains foundational to statistical mechanics despite lasting debate over its reconciliation with the time-reversibility of the underlying particle dynamics.

Facts
Statement
The H-theorem describes the tendency of the quantity H to decrease in a nearly ideal gas of molecules. 1
Proof Year
1872 1
Classification
Statement Form
Inequality 1
Connections

Has Statement Form

Inequality, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Proved By

Source H-theorem, Wikipedia
Sources
1. H-theorem, Wikipedia
  • Lead section
    the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency of the quantity H (defined below) to decrease in a nearly-ideal gas of molecules.
  • Proved By: Ludwig Boltzmann, Lead paragraph
    In classical statistical mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency of the quantity H (defined below) to decrease in a nearly-ideal gas of molecules. As this
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