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.

Background: Brain connectivity has shown to be a key characteristic in the study of both Parkinson’s Disease (PD) and the response of the patients to the dopaminergic medication. Time series analysis has been used here for the first time to study brain connectivity changes during motor activation in PD. Methods: A 64-channel EEG signal was registered during unilateral motor activation and resting-state in 6 non-demented PD patients before and after the administration of levodopa and in 6 matched healthy controls. Spectral entropy correlation, coherence, and interhemispheric divergence differences among PD patients and controls were analyzed under the assumption of stationarity of the time series. Results: During the motor activation test, PD patients showed an increased correlation coefficient (both hands p < 0.001) and a remarkable increase in coherence in all frequency range compared to the generalized reduction observed in controls (both hands p < 0.001). The Kullback­–Leibler Divergence (KLD) of the Spectral Entropy between brain hemispheres was observed to increase in controls (right hand p = 0.01; left hand p = 0.015) and to decrease in PD patients (right hand p = 0.02; left hand p = 0.002) with motor activation. Conclusions: Our results suggest that the oscillatory activity of the different cortex areas within healthy brains is relatively independent of the rest. PD brains exhibit a stronger connectivity which grows during motor activation. The levodopa mitigates this anomalous performance.

Embedding living polymers that consume chemical energy into synthetic gels offers a route to soft materials that self‐regulate their mechanical state. Here, The bacterial cytokinetic protein FtsZ is integrated within a polyacrylamide network to create an active extensile hydrogel. Upon post‐gelation activation with Mg ² ⁺ and GTP, FtsZ filaments treadmill and exert internal stresses that drive isotropic swelling and mechanical softening. These responses is described using a Flory–Rehner swelling framework, where activity‐induced volume expansion lowers the polymer volume fraction and, consequently, the elastic modulus. Normalizing the measured moduli to the FR baseline isolates an additional, rate‐dependent softening that arises from living FtsZ polymer dynamics. Rheological analysis reveals that biochemical energy input modulates the elastic state of a pre‐formed network through active swelling and strain‐dependent fluidization, establishing a minimal model for living‐polymer‐driven soft materials.

Red blood cells (RBCs) sustain mechanical stresses associated with microcirculatory flow through ATP‐driven plasma membrane flickering. This is an active phenomenon driven by motor proteins that regulate interactions between the spectrin cytoskeleton and the lipid bilayer; it is manifested in RBC shape fluctuations reflecting the cell's mechanical and metabolic state. Yet, direct quantification of the forces and energetic costs underlying this non‐equilibrium behavior remains challenging due to the invasiveness of existing techniques. Here, a minimally invasive method that combines bead‐free, low‐power optical tweezers with high‐speed video microscopy is employed to track local membrane forces and displacements in single RBCs during the same time window. This independent dual‐channel measurement enables the construction of a mechano‐dynamic phase space for RBCs under different chemical treatments, which allows for differentiating between metabolic and structural states based on their fluctuation‐force signatures. Quantification of mechanical work during flickering demonstrates that membrane softening enhances fluctuations while elevating energy dissipation. The proposed optical tweezers methodology provides a robust framework for mapping the active mechanics of living cells, enabling precise probing of cellular physiology and detection of biomechanical dysfunction in diseases.