Irreversibility of classical fluctuations studied in analogue electrical circuits

Fluctuations around some average or equilibrium state arise universally in physical systems. Large fluctuations — fluctuations that are much larger than average — occur only rarely but are responsible for many physical processes, such as nucleation in phase transitions, chemical reactions, mutations in DNA sequences, protein transport in cells and failure of electronic devices. They lie at the heart of many discussions1,2,3,4,5 of how the irreversible thermodynamic behaviour of bulk matter relates to the reversible (classical or quantum-mechanical) laws describing the constituent atoms and molecules. Large fluctuations can be described theoretically using hamiltonian6,7 and equivalent path-integral8,9,10,11,12 formulations, but these approaches remain largely untested experimentally, mainly because such fluctuations are rare and also because only recently was an appropriate statistical distribution function formulated11. It was shown recently, however, that experiments on fluctuations using analogue electronic circuits allow the phase-space trajectories of fluctuations in a dynamical system to be observed directly12. Here we show that this approach can be used to identify a fundamental distinction between two types of random motion: fluctuational motion, which takes the system away from a stable state, and relaxational motion back towards this state. We suggest that macroscopic irreversibility is related to temporal asymmetry of these two types of motion, which in turn implies a lack of detailed balance and corresponds to non-differentiability of the generalized nonequilibrium potential in which the motion takes place.