Generalizing Landauer’s principle

In a recent paper [Stud. Hist. Philos. Mod. Phys. 36, 355 (2005)] it is argued that to properly understand the thermodynamics of Landauer’s principle it is necessary to 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 Landauer 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 its universality, extending considerably the validity of previous proofs. This confirms conjectures made that all logical operations may, in principle, be performed in a thermodynamically reversible fashion, although logically irreversible operations would require special, practically rather difficult, conditions to do so. 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 special cases of our generalized principle.

Figure 1

Arranging input states.

Figure 2

Inserting subpartitions.

Figure 3

Rearranging the partitions.

Figure 4

Arranging the output states