The Fluctuation-Dissipation Theorem Today

We revisit the concept of fluctuations in equilibrium and non-equilibrium statistical mechanics. Although the relationship between fluctuations and dissipation, established in terms of the so-called fluctuation-dissipation theorem (FDT) and formulating links between nonequilibrium phenomena and time correlations of spontaneous fluctuations (at equilibrium), has been widely investigated over the past 50 years, some violations of that casual relation are still often found in literature and present controversial facets calling for further corrections and generalizations. As an example, in generic quantum systems FDT has been recently shown to be directly related to quantum metrology in systems with non-equilibrium states.
Moreover, with the crescent abilities of experimentalists to work in small scales and at low temperatures those quantum versions of fluctuation-dissipation (FD) relations need to be better understood. At the same time techniques used to study disordered system (spin glasses, Almeida-Thouless transition etc...) and nonlinear dynamics (KPZ, turbulence...) exhibit a basic similar mathematical structure, able to find linear response and FD solutions for fundamental physics, such as string theories, quantum chaos and information theory. Important practical applications stem from those new tools, such as telecommunications, biophysics, finance and machine learning.

We expect that the authors contribute with new original works or reviews where fluctuation-dissipation relations appears. Interdisciplinary aspects are widely welcome.