A persistent object is an object that survives reboot. On Unix, files and directories are persistent but processes and file descriptors are not. EROS is an example of an orthogonally persistent system: processes and capabilities also survive reboot. To a process, it generally only looks as if it had not been scheduled for a long time; the rest of its environment remains essentially the indistinguishable.
GNU/Hurd
The GNU/Hurd is not a persistent system: there are no persistent capabilities. All data that is stored in files in the file system, is serialized.
Further Reading
shapiro capintro 1999: What is a Capability, Anyway?, Jonathan Shapiro, 1999. This is an easily readable introduction with good examples. In the author's own words, the text provides a layman's introduction to capabilities, describing what they are, what they do, and why they result in better security than today's computer systems.
Section Writing Things Down in [shapiro_capintro_1999].