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Negative Specific Heat: Long-Range vs Short-Range Gas

A self-gravitating (long-range) toy gas vs a short-range contact gas: slowly remove energy from each and watch the caloric curve — one bends backward (temperature rises as energy drops), the other behaves normally.

Physics & Mechanics3DAdvanced60 FPS

Details

CategoryPhysics & Mechanics

RenderingThree.js · WebGL

DifficultyAdvanced

Target FPS60

ControlsToggle between long-range (self-gravitating) and short-range (contact gas) interaction modes; energy-budget slider to drain or add total energy as a slow reservoir; Auto sweep button to scan the slider automatically; Clear curve button; orbit camera on the 3D particle cloud; live stat boxes for energy, temperature, core density and a normal/anomalous specific-heat-sign badge.

negative specific heatnon-extensive statistical mechanicslong-range interactionsself-gravitating gasensemble inequivalencecaloric curvevirial theorem

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A toy N-body gas confined to a spherical container, switchable between a long-range (self-gravitating) interaction and a short-range (contact) interaction. Slowly draining or adding energy traces a live caloric curve — for the long-range gas it bends backward, so temperature rises as energy is removed, the hallmark of negative specific heat and ensemble inequivalence in non-additive statistical-mechanical systems.

⚙ Under the hood

An N-body toy gas confined to a sphere, switchable between a long-range self-gravitating interaction and a short-range contact-gas interaction. Slowly drain or add energy with a slider and watch a live (energy, temperature) caloric curve trace itself — the long-range gas collapses into a dense core and its temperature rises as energy is removed, bending the curve backward into negative specific heat, while the short-range gas cools normally and the curve never bends.

negative specific heatnon-extensive statistical mechanicslong-range interactionsself-gravitating gasensemble inequivalencecaloric curvevirial theorem

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install