  In a recent paper [Mar05] it is argued that to properly understand the
thermodynamics of Landauer's Principle it is necessary extend the concept of
logical operations to include indeterministic operations. Here we examine the
thermodynamics of such operations in more detail, extending the work of
Landuaer[Lan61] to include indeterministic operations and to include logical
states with variable entropies, temperatures and mean energies. We derive the
most general statement of Landauer's Principle and prove it's universality,
extending considerably the validity of previous proofs. This confirms
conjectures made in [Mar05b], in particular that all logical operations may, in
principle, be performed in a thermodynamically reversible fashion. We
demonstrate a physical process that can perform any computation without work
requirements or heat exchange with the environment. Many widespread statements
of Landauer's Principle are shown to be only special cases of our generalised
principle.
