Biological machines fascinate and inspire with unexpected engineering solutions on a molecular scale. Motor proteins are one famous example, generating rotary or linear mechanical work from chemical energy isothermally. One dimension up are pumps that generate chemical potential gradients between cellular compartments. Of these, the nuclear pore is the largest and most versatile. It separates the cytoplasm from the nucleus, and regulates the traffic of proteins and RNAs. Soluble receptors facilitate the passage of their cargo through the pore. The system of pore and receptors can work against soluble concentration gradients. How to understand this function as a chemically-selective pump presents an important challenge in cellular biophysics. On one hand there is a source of chemical energy in GTP hydrolysis, while on the other, there is no force-generating element or obvious mechanical movement involved. An in vitro system of cell-free nuclei reconstituted in Xenopus laevis egg extract provides an ideal environment to test the system thermodynamically. A combination of classical kinetic measurements by confocal fluorescence microscopy, correlation spectroscopy, and photobleaching reveal an unexpectedly simple behavior. An interpretation in the spirit of classical enzymology suggests a novel paradigm for molecular exchange between the nucleus and cytoplasm.