SWhat changed
Particles can keep moving while obeying a simple long-run energy balance. Clausius related the time-averaged kinetic energy of bounded stationary motion to a force-position quantity he called the virial. His mechanical derivation keeps a time-boundary term before taking a periodic or long-time average. For central pair forces and uniform external pressure, it connects microscopic motion with the pressure-volume term.
Scientific scope
Particles can keep moving while obeying a simple long-run energy balance. Clausius related the time-averaged kinetic energy of bounded stationary motion to a force-position quantity he called the virial. His mechanical derivation keeps a time-boundary term before taking a periodic or long-time average. For central pair forces and uniform external pressure, it connects microscopic motion with the pressure-volume term. The stationary setting bounds positions and velocities and requires the relevant averages or periodic averages to be meaningful. A small boundary term alone does not establish existence of every time average or a general ergodic theorem. In the original convention, vis viva is one-half mass times speed squared; the uniform-pressure contribution is 3pV/2. Pair-force and molecular phase-average specializations retain their additional assumptions. This mechanical contribution differs from Clausius entropy theory and later astronomical applications. The source is a contemporary English translation, not a claim of identical German-source bytes.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The stationary setting bounds positions and velocities and requires the relevant averages or periodic averages to be meaningful. A small boundary term alone does not establish existence of every time average or a general ergodic theorem. In the original convention, vis viva is one-half mass times speed squared; the uniform-pressure contribution is 3pV/2. Pair-force and molecular phase-average specializations retain their additional assumptions. This mechanical contribution differs from Clausius entropy theory and later astronomical applications. The source is a contemporary English translation, not a claim of identical German-source bytes.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.5. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
Full scientific record · Browse contribution grades · Request a correction