  In thermodynamics one considers thermal systems and the maximization of
entropy subject to the conservation of energy. A consequence is Landauer's
erasure principle, which states that the erasure of 1 bit of information
requires a minimum energy cost equal to $kT\ln(2)$ where $T$ is the temperature
of a thermal reservoir used in the process and $k$ is Boltzmann's constant.
Jaynes, however, argued that the maximum entropy principle could be applied to
any number of conserved quantities which would suggest that information erasure
may have alternative costs. Indeed we showed recently that by using a reservoir
comprising energy degenerate spins and subject to conservation of angular
momentum, the cost of information erasure is in terms of angular momentum
rather than energy. Here we extend this analysis and derive the minimum cost of
information erasure for systems where different conservation laws operate. We
find that, for each conserved quantity, the minimum resource needed to erase 1
bit of memory is $\lambda^{-1}\ln(2)$ where $\lambda$ is related to the average
value of the conserved quantity. The costs of erasure depend, fundamentally, on
both the nature of the physical memory element and the reservoir with which it
is coupled.
