A study is made of the entropy of a random-flight polymer confined in a box of volume V. When the natural radius of the polymer approaches the linear size of the box, the entropy ceases to have the normal form of a thermodynamic function and the pressure is not a function of the density but takes the form PV= pi 2/3(Ll/R2) kappa T where L is the polymer length, l the step length and R equals V, and the density of the system even though strictly in equilibrium is not uniform. The introduction of constraints due to forces, cross linkages and very long-lived quasi-invariants restores the equation of state to a thermodynamic form P=P( rho ) where rho =L/Vl.
