We present results connecting the fluctuations of small-scalethermodynamics with information processing and computation. To begin, we experimentally demonstrate that highly structured distributions of work emerge during even the simple task of erasing a single bit. These are signatures of a refined suite of time-reversal symmetries in distinct functional classes of microscopic trajectories. As a consequence, we introduce the Trajectory Class Fluctuation Theorem (TCFT), a deep fluctuation theorem that the component work distributions must satisfy. Since they identify entropy production, the component work distributions encode both the frequency of various mechanisms of success and failure during computing as well as giving improved estimates of the total irreversibly-dissipated heat. This new diagnostic tool provides strong evidence that thermodynamic computing at the nanoscale can be constructively harnessed. We experimentally verify this functional decomposition and the new class of fluctuation theorems by measuring transitions between flux states in a superconducting circuit.

The TCFT provides broader insights.It substantially strengthens the Second Law of Thermodynamics and its consequences. Practically, the TCFT improves empirical estimates of free energies, a task known to be statistically challenging. It reveals the thermodynamics induced by macroscopic system transformations for each measurable subset of system trajectories. In this, it directly combats the statistical challenge of extremely rare events that dominate thermodynamic calculations. And, it reveals new forms of free energy---forms that can be solved analytically and practically estimated. For engineered systems, it provides a toolkit for diagnosing the thermodynamics responsible for system functionality. Conceptually, the TCFT unifies a host of previously-established fluctuation theorems, interpolating from Crooks' Detailed Fluctuation Theorem (single trajectories) to Jarzynski's Equality (full trajectory ensembles).

We further utilize fluctuation theory to construct new thermodynamic boundsfor systems controlled with a time-symmetric protocol, again studying bit erasure in detail. We demonstrate that the bounds are tight and show that the costs overwhelm those implied by Landauer's energy bound on information erasure. Moreover, in the limit of perfect computation, the costs diverge. A takeaway is that time-asymmetric protocols should be developed for efficient, accurate thermodynamic computing. And, that Landauer's Stack---the full suite of theoretically-predicted thermodynamic costs---is ready for experimental test and calibration.