Trajectory-Class Fluctuation Theorems: Work Decomposition in Metastable Information Processing

Information processing is physical. It requires particular and precise control of the underlying thermodynamic system. While system parameters in a cyclic control protocol begin and end in the same configuration, their intermediate paths determine the evolution of the system's informational states.
The full work distribution generated during thermodynamic computing is surprisingly complex. Even if simple, efficient, and accurate, the effective information processing may exhibit thermodynamically-distinct temporal substages. For example, a bit erasure protocol similar to that of Jun et. al. (2014 PRL 113.190601) consists of four substages, each linearly changing a single protocol parameter. Combining substage decomposition with partitioning the microscopic state-space into thermodynamically-metastable regions, a symbolic dynamics emerges that naturally decomposes the work distribution into canonical components, with each substage obeying its own fluctuation theorems. Practically, through describing macroscopic observables, such as net work, these components can be used to diagnose the predominance of specific microscopic informational failure and success modes. In this way, the trajectory-class fluctuation theorems can be used to guide optimal protocol design.