| 1. | This semigroup evolves according to the one-dimensional heat equation:
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| 2. | The heat equation is of fundamental importance in diverse scientific fields.
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| 3. | A physical interpretation of this principle comes from the heat equation.
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| 4. | Derivation of the heat equation from Fourier's law.
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| 5. | The heat will therefore diffuse according to the 1-D heat equation.
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| 6. | When applying this transformation, the heat equation becomes:
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| 7. | Clearly, the following expression is also a solution of the heat equation:
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| 8. | The heat equation is a partial differential equation.
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| 9. | Equation 1 can now be related to the specific heat equation for constant volume.
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| 10. | The equation for this is shown below and is similar to the Heat equation.
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