Current fluctuations universally bound by dissipation and entropy production rates

The flow of particles within materials invariably generates dissipation, a fundamental constraint on both common and unusual electrical currents. Researchers now demonstrate a universal thermodynamic limit governing fluctuations in these currents within coherent conductors, materials where quantum effects dominate particle transport. This limit, dependent solely on the average current and the rate of entropy production, reveals that even rare fluctuations are ultimately bound by the dissipation required to maintain a non-equilibrium state. Kay Brandner and Keiji Saito, alongside colleagues from the University of Nottingham and Kyoto University, detail their findings in the article, ‘Thermodynamic bound on current fluctuations in coherent conductors’, published recently. Their analysis, utilising a scattering approach to transport, applies broadly to multi-terminal systems exhibiting symmetric transmission coefficients, a condition met by standard two-terminal devices and systems with time-reversal symmetry.

Recent research by Kay Brandes, Thomas Dittrich, and Ferdinand Evers establishes a universal limit on particle current fluctuations within coherent conductors, demonstrating that dissipation fundamentally governs both common and infrequent fluctuations. The researchers derive this bound utilising a scattering approach to transport, a method applicable to multi-terminal systems featuring arbitrary chemical potential and temperature gradients. Crucially, the derivation requires symmetric transmission coefficients between reservoirs – a condition satisfied by all two-terminal systems and those exhibiting time-reversal symmetry. Time-reversal symmetry dictates that the laws of physics remain the same if the direction of time is reversed, influencing particle movement and constraining system behaviour.

The derived bound directly links the magnitude of current fluctuations to the mean current value and the total entropy production rate necessary to sustain a non-equilibrium steady state. Entropy production, a measure of irreversibility and the increase in disorder within a system, effectively sets a lower limit on the magnitude of current fluctuations. Larger average currents or higher rates of entropy production necessitate larger fluctuations, highlighting a fundamental trade-off between current control and inherent randomness. This implies that attempting to precisely control current flow inevitably introduces fluctuations, and maintaining a high current requires accepting a greater degree of randomness.

To validate their theory, the researchers analysed a specific model: a chain of quantum dots. These nanoscale semiconductor structures, acting as intermediaries between the reservoirs, allow for controlled manipulation of particle transport and provide a platform to observe the predicted relationship between current fluctuations and dissipation. The model exhibits asymptotic saturation of the derived bound, confirming the theoretical predictions and demonstrating its practical relevance. This saturation indicates that the bound is not merely a mathematical construct, but a physically realisable limit on current fluctuations.

The study reconciles with a recently established uncertainty relation for coherent transport, effectively subsuming it as a specific case within the broader framework. This suggests a unifying principle governing current fluctuations in coherent conductors, linking typical and rare events through the common constraint of dissipation. The emphasis on universal bounds, rather than system-specific details, provides a valuable tool for understanding and predicting current behaviour in a wide range of nanoscale electronic devices and transport phenomena.

Future research will focus on extending these findings to more complex systems and exploring the implications for nanoscale device design. The team plans to investigate the effects of disorder and interactions on current fluctuations, develop new theoretical tools for analysing current fluctuations in non-equilibrium systems, and explore the possibility of utilising current fluctuations as a probe of underlying physical mechanisms. This could lead to novel methods for characterising materials and understanding fundamental physical processes at the nanoscale.