  The statistical state of any (classical or quantum) system with non-trivial
time evolution can be interpreted as the pointer of a clock. The quality of
such a clock is given by the statistical distinguishability of its states at
different times. If a clock is used as a resource for producing another one the
latter can at most have the quality of the resource. We show that this
principle, formalized by a quasi-order, implies constraints on many physical
processes. Similarly, the degree to which two (quantum or classical) clocks are
synchronized can be formalized by a quasi-order of synchronism.
  Copying timing information is restricted by quantum no-cloning and
no-broadcasting theorems since classical clocks can only exist in the limit of
infinite energy. We show this quantitatively by comparing the Fisher timing
information of two output systems to the input's timing information. For
classical signal processing in the quantum regime our results imply that a
signal looses its localization in time if it is amplified and distributed to
many devices.
