where formula_42 is a fixed constant. Let us call formula_43 the force exerted by the chain on the point to which its end is attached. From the above expression of the entropy, we can deduce an expression of this force. Suppose that, instead of being fixed, the positions of the two ends of the ideal chain are now controlled by an operator. The operator controls the evolution of the end to end vector formula_2. If the operator changes formula_2 by a tiny amount formula_46, then the variation of internal energy of the chain is zero, since the energy of the chain is constant. This condition can be written as: