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.