Thinking·OS
← Back
In graph Frontier
Statistical PhysicsEstablished

Boltzmann distribution

The Boltzmann distribution gives the probability of a system occupying a state as an exponential function of its energy and temperature.

Boltzmann distributionMicrostateCanonical ensemblePartition functionEquipartition theoremMacrostateEntropyStatistical ensembleTemperature

At a glance

Type
energy
Disciplines 1
Statistical Physics
Mental models 0
—
Role in the graph
Connector

Key signals

Cross-disciplinary reach
Disciplines
1
  • Statistical Physics
Evidence & development

Dependencies

What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.

Foundations · builds on

Boltzmann distributionis derived fromCanonical ensembleEstablished

Open Canonical ensemble →

Boltzmann distribution is derived from Canonical ensemble.

Enables · leads to

Equipartition theoremis derived fromBoltzmann distributionEstablished

Open Equipartition theorem →

Equipartition theorem is derived from Boltzmann distribution.

Partition functionis derived fromBoltzmann distributionEstablished

Open Partition function →

Partition function is derived from Boltzmann distribution.

Structural role & consequence

Interpreted from the current atlas graph — what the connections mean, not just how many there are.

  • Currently dark in the atlas: no key date stored · 4 of 4 of its relations lack claim-level evidence.

    atlas representation · Describes the current Thinking OS representation, not the state of the world.

  • Builds on 1 foundation (requires / depends-on / derived-from / emerges-from).

    structural · Structural graph analysis — not a claim of importance, causation or history.

  • Structural neighbourhood: 4 → 9 → 31 concepts reachable within 3 hops.

    structural · Structural reach — being reachable is not the same as being understood.

  • All 4 of its relationships stay within its own discipline — a field-specific concept in the current atlas.

    structural · Structural graph analysis — not a claim of importance, causation or history.

0%

cross-field
4 within-field, 0 cross-field

0 of 4 relations carry evidence · concept has a verified source

Strengths & constraints

Constraints

  • Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
  • No dated history stored — the atlas records no key date for this concept. atlas representation

Conditions

  • Its dependency reading rests on 1 foundation relation. structural
  • Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural

Dependency radial

What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.

Canonical ensembleEquipartition theoremPartition functionBoltzmann distribution◀ builds onenables ▶

Seen through each discipline

How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.

Statistical Physics

Through this lens it connects to Microstate, Canonical ensemble, Partition function and Equipartition theorem.

Boltzmann distribution through the Statistical Physics lens →

Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.

The scientific picture
  • Connects 4 other ideas across 1 discipline.
  • Most of its connections are of the “Dependency” kind.

Derived from the graph’s real structure — observations, not a score.

Sources