Dear Colleagues,

Our understanding of fluctuations in small nonequilibrium systems has been significantly advanced owing to the development of stochastic and quantum thermodynamics. One of the prominent results in recent years is the thermodynamic uncertainty relation (TUR), which indicates a trade-off relation between the precision of currents and thermodynamic cost quantified via irreversible entropy production. Initially derived for stationary Markov processes in the linear response regime, it has now been generalized for generic initial states under arbitrary time-dependent driving and also extended to the quantum regime, including quantum effects such as quantum coherence. The TUR is not only theoretically important (e.g., implications on the trade-off between the power and efficiency of steady-state heat engines, and the extent of anomalous diffusion), but it has also found a practical application in the thermodynamic inference of dissipation.

Given the importance and significance of the TUR, this Special Issue aims at providing a focus on the TUR from both theoretical and experimental aspects, ranging from biophysics to classical and quantum physics. This includes but is not limited to exploring generalizations to other dynamics, novel TUR-like tradeoffs between precision and cost, theoretical and practical applications, and quantum effects.

Dr. Tan Van Vu
Prof. Dr. Keiji Saito
Guest Editors

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• entropy production
• current fluctuation
• thermodynamic trade-off relations
• stochastic thermodynamics
• quantum thermodynamics