Relative fluctuations of observables in discrete stochastic systems are bounded at all times by the mean dynamical activity in the system, quantified by the mean number of jumps. This constitutes a kinetic uncertainty relation that is fundamentally different from the thermodynamic uncertainty relation recently discussed in the literature. The thermodynamic constraint is more relevant close to equilibrium while the kinetic constraint is the limiting factor of the precision of a observables in regimes far from equilibrium. This is visualized for paradigmatic simple systems and with an example of molecular motor dynamics. Our approach is based on the recent fluctuation response inequality by Dechant and Sasa (2018 arXiv:1804.08250) and can be applied to generic Markov jump systems, which describe a wide class of phenomena and observables, including the irreversible predator-prey dynamics that we use as an illustration.

Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.

The folding of a protein towards its native state is a rather complicated process. However, there is empirical evidence that the folding time correlates with the contact order, a simple measure of the spatial organization of the native state of the protein. Contact order is related to the average length of the main chain loops formed by amino acids that are in contact. Here we argue that folding kinetics can also be influenced by the entanglement that loops may undergo within the overall three-dimensional protein structure. In order to explore such a possibility, we introduce a novel descriptor, which we call ‘maximum intrachain contact entanglement’. Specifically, we measure the maximum Gaussian entanglement between any looped portion of a protein and any other non-overlapping subchain of the same protein, which is easily computed by discretized line integrals on the coordinates of the C α atoms. By analyzing experimental data sets of two-state and multi-state folders, we show that the new index is also a good predictor of the folding rate. Moreover, being only partially correlated with previous methods, it can be integrated with them to yield more accurate predictions.

There does not exist a general positive correlation between important life-supporting properties and the entropy production rate. The simple reason is that nondissipative and time-symmetric kinetic aspects are also relevant for establishing optimal functioning. In fact those aspects are even crucial in the nonlinear regimes around equilibrium where we find biological processing on mesoscopic scales. We make these claims specific via examples of molecular motors, of circadian cycles and of sensory adaptation, whose performance in some regimes is indeed spoiled by increasing the dissipated power. We use the relation between dissipation and the amount of time-reversal breaking to keep the discussion quantitative also in effective models where the physical entropy production is not clearly identifiable.