text: The case of an ideal chain whose two ends are attached to fixed points will be considered in this sub-section. The vector  joining these two points characterizes the macroscopic state (or macro-state) of the ideal chain. Each macro-state corresponds a certain number of micro-states, that we will call  (micro-states are defined in the introduction to this section). Since the ideal chain's energy is constant, each of these micro-states is equally likely to occur. The entropy associated to a macro-state is thus equal to:
  where  is Boltzmann's constant
  The above expression gives the absolute (quantum) entropy of the system. A precise determination of  would require a quantum model for the ideal chain, which is beyond the scope of this article. However, we have already calculated the probability density  associated with the end-to-end vector of the unconstrained ideal chain, above. Since all micro-states of the ideal chain are equally likely to occur,  is proportional to . This leads to the following expression for the classical (relative) entropy of the ideal chain:
  where  is a fixed constant. Let us call  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 . If the operator changes  by a tiny amount , 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:
   is defined as the elementary amount of mechanical work transferred by the operator to the ideal chain, and  is defined as the elementary amount of heat transferred by the solvent to the ideal chain. Now, if we assume that the transformation imposed by the operator on the system is quasistatic (i.e., infinitely slow), then the system's transformation will be time-reversible, and we can assume that during its passage from macro-state  to macro-state , the system passes through a series of thermodynamic equilibrium macro-states. This has two consequences:
  # first, the amount of heat received by the system during the transformation can be tied to the variation of its entropy:  where  is the temperature of the chain.
  # second, in order for the transformation to remain infinitely slow, the mean force exerted by the operator on the end points of the chain must balance the mean force exerted by the chain on its end points. Calling  the force exerted by the operator and  the force exerted by the chain, we have: 
  We are thus led to:
  The above equation is the equation of state of the ideal chain. Since the expression depends on the central limit theorem, it is only exact in the limit of polymers containing a large number of monomers (that is, the thermodynamic limit).  It is also only valid for small end-to-end distances, relative to the overall polymer contour length, where the behavior is like a hookean spring.  Behavior over larger force ranges can be modeled using a canonical ensemble treatment identical to magnetization of paramagnetic spins. For the arbitrary forces the extension-force dependence will be given by Langevin function :
  where the extension is .
  For the arbitrary extensions the force-extension dependence can be approximated by:
  where  is the inverse Langevin function,  is the number of bonds in the molecule (therefore if the molecule has  bonds it has  monomers making up the molecule.).
  Finally, the model can be extended to even larger force ranges by inclusion of a stretch modulus along the polymer contour length.  That is, by allowing the length of each unit of the chain to respond elastically to the applied force.