Relations between entropies produced in nondeterministic thermodynamic processes

Landauer’s erasure principle is generalized to nondeterministic processes on systems having an arbitrary number of nonsymmetrical logical states. The condition that the process is applied in the same way, irrespective of the initial logical state, imposes some restrictions on the individual heat exchanges associated with each possible transition. The complete set of such restrictions are derived by a statistical analysis of the phase-space flow induced by the process. Landauer’s erasure principle can be derived from and is a special case of these.

Figure 1

The steps of the process on a single molecule system with $n=2$ initial and $m=3$ final logical states. The system is prepared in initial configuration and (1) potentials of each region are lowered to zero, (2) additional walls are inserted, (3) volume of each region is expanded or compressed, (4) some parts of the walls are removed, (5) walls are aligned at constant volume, (6) each region is compressed adiabatically by pistons from left, (7) small holes opened on the pistons to let the molecule expand freely toward the left part, and finally (8) pistons are removed and the potentials of each region are increased.