Speaker
Description
We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of diffusion on all time scales in equilibrium or non-equilibrium steady states [1,2] and for transient or non-ergodic dynamics [3]. The time averaging and coarse graining hardwired in the definition of the functionals under consideration give rise to experimentally relevant but highly non-trivial statistics. We unravel a deep connection between current fluctuations and generalized time-reversal symmetry. We highlight the essential role of coarse graining in space from mathematical, thermodynamical, and experimental points of view. Spatial coarse graining is required to uncover salient features of currents that break detailed balance, and a thermodynamically ``optimal'' coarse graining ensures the most precise inference of dissipation. The results and employed methods give a new view on the Thermodynamic Uncertainty Relation [4]. Defined without coarse graining, the fluctuations of empirical density and current are proven to diverge on all time scales in dimensions higher than one, which has far-reaching consequences for large-deviation limits in continuous space. Our findings provide new intuition about time-averaged observables and allow for a more efficient analysis of single-molecule experiments.
[1] Phys. Rev. Lett. 129, 140601 (2022)
[2] Phys. Rev. Research 4, 033243 (2022)
[3] J. Phys. A: Math. Theor. 55, 475001 (2022)
[4] Phys. Rev. Lett. 130, 087101 (2023)
