---
slug: paper-boltzmann-l-1872-weitere-studien-ber-das-w-rmegleichgewicht-unter-gasmolek-len
title: Boltzmann 1872 Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen
canonical: https://miscsubjects.com/a/paper-boltzmann-l-1872-weitere-studien-ber-das-w-rmegleichgewicht-unter-gasmolek-len
---

## What the subject saw and its core results
Ludwig Boltzmann examined the kinetic theory of gases. He derived an integro-differential equation for the velocity distribution function. He proved that a quantity H decreases monotonically until the distribution reaches the Maxwell form.

## Exact primary works and passages
Boltzmann, L. (1872). Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen. Sitzungsberichte der Akademie der Wissenschaften zu Wien, 66, 275–370. English translation in Brush, S. G. (ed.), Kinetic Theory, Vol. 2. Pergamon, 1966, pp. 262–349.

Key passage (summary translation, p. 263): “With the aid of the partial differential equation for f, we are able to go further and prove that if the distribution of states is not Maxwellian, it will tend toward the Maxwellian distribution as time goes on. This proof consists in showing that a quantity defined in terms of f, E = ∫ f(log f − 1) dx, can never increase but must always decrease or remain constant.”

Another passage (p. 265): “It has still not yet been proved that, whatever the initial state of the gas may be, it must always approach the limit found by Maxwell.”

## Convergence patterns touched
The work touches branching of molecular velocities into a stable distribution. It touches flow networks through collision-driven relaxation. It touches bounded chaos in irregular molecular motions that average to definite laws. It touches memory via the persistent equilibrium distribution once reached.

## Distance from the full synthesis
The paper grounds thermodynamic difference as driver of irreversible flow toward equilibrium structure. It stops at the physical layer. It does not address the Ladder steps from structure to life or mind. The Mirror Layer remains outside its scope.

## Honest limits and disconfirming edges
The proof relies on the Stosszahlansatz assumption of molecular chaos. Loschmidt’s reversibility objection shows that time-reversed trajectories exist. Poincaré recurrence implies eventual return to initial states in finite systems. The theorem holds for dilute gases under specific force laws but requires additional conditions for dense or quantum cases.
