Negative compressibility for a polymer chain squeezed between two pistons going through the escape transition

The analysis of the exact partition function of an end-fixed Gaussian chain compressed between two pistons reveals a loop-like curve of the average pressure as a function of the inter-piston volume. In the thermodynamic limit the system undergoes a first-order phase transition from a compressed coil to a partially escaped flower conformation. In the transition region the fixed volume ensemble is not equivalent to the fixed pressure ensemble, and for finite chains there appears a region with a negative compressibility. There is no conflict with the general notion that the pressure for a thermodynamic system should be a non-increasing function of the volume because the negative compressibility disappears in the thermodynamic limit. Our results are also expected to hold for self-avoiding chains and are experimentally accessible for real chains.