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→Independent degrees of freedom
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==Independent degrees of freedom==
== Independent degrees of freedom 独立自由度 ==
The set of degrees of freedom {{math|''X''<sub>1</sub>, ... , ''X''<sub>''N''</sub>}} of a system is independent if the energy associated with the set can be written in the following form:
The set of degrees of freedom {{math|''X''<sub>1</sub>, ... , ''X''<sub>''N''</sub>}} of a system is independent if the energy associated with the set can be written in the following form:
* If <math>E = X_1^4 + X_2^4</math>, then the two degrees of freedom are independent.
* If <math>E = X_1^4 + X_2^4</math>, then the two degrees of freedom are independent.
* If <math>E = X_1^4 + X_2^4</math>, then the two degrees of freedom are independent.
* If <math>E = X_1^4 + X_1 X_2 + X_2^4</math>, then the two degrees of freedom are ''not'' independent. The term involving the product of {{math|''X''<sub>1</sub>}} and {{math|''X''<sub>2</sub>}} is a coupling term that describes an interaction between the two degrees of freedom.
* If <math>E = X_1^4 + X_1 X_2 + X_2^4</math>, then the two degrees of freedom are not independent. The term involving the product of and is a coupling term that describes an interaction between the two degrees of freedom.
* If <math>E = X_1^4 + X_1 X_2 + X_2^4</math>, then the two degrees of freedom are not independent. The term involving the product of and is a coupling term that describes an interaction between the two degrees of freedom.