 Entropy concavity and positive heat capacity

ID: entropy-concavity-and-positive-heat-capacity

For a thermodynamically stable system, the entropy is concave in energy, so

\frac{\partial ^{2} S}{\partial E ^{2}} = - \frac{1}{T ^{2}} \frac{\partial T}{\partial E} < 0.

Consequently

\partial E / \partial T > 0

: energy increases with temperature, and the corresponding heat capacity is positive.

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