Fluctuations and like-torque clusters at the onset of the discontinuous shear thickening transition in granular materials

The main mechanism driving rheological transitions is usually mechanical perturbation by shear unjamming mechanism. Investigating discontinuous shear thickening is challenging because the shear counterintuitively acts as a jamming mechanism. Moreover, at the brink of this transition, a thickening material exhibits fluctuations that extend both spatially and temporally. Despite recent extensive research, the origins of such spatiotemporal fluctuations remain unidentified. Here, we numerically investigate the fluctuations in injected power in discontinuous shear thickening in granular materials. We show that a simple fluctuation relation governs the statistics of power fluctuations. Furthermore, we reveal the formation of like-torque clusters near thickening and identify an unexpected relation between the spatiotemporal fluctuations and the collective behavior due to the formation of like-torque clusters. We expect that our general approach should pave the way to unmasking the origin of spatiotemporal fluctuations in discontinuous shear thickening.

Testing the Steady-State Fluctuation Relation in the Solar Photospheric Convection

The turbulent thermal convection on the Sun is an example of an irreversible non-equilibrium phenomenon in a quasi-steady state characterized by a continuous entropy production rate. Here, the statistical features of a proxy of the local entropy production rate, in solar quiet regions at different timescales, are investigated and compared with the symmetry conjecture of the steady-state fluctuation theorem by Gallavotti and Cohen. Our results show that solar turbulent convection satisfies the symmetries predicted by the fluctuation relation of the Gallavotti and Cohen theorem at a local level.

Fluctuation relations and fitness landscapes of growing cell populations

We construct a pathwise formulation of a growing population of cells, based on two different samplings of lineages within the population, namely the forward and backward samplings. We show that a general symmetry relation, called fluctuation relation relates these two samplings, independently of the model used to generate divisions and growth in the cell population. Known models of cell size control are studied with a formalism based on path integrals or on operators. We investigate some consequences of this fluctuation relation, which constrains the distributions of the number of cell divisions and leads to inequalities between the mean number of divisions and the doubling time of the population. We finally study the concept of fitness landscape, which quantifies the correlations between a phenotypic trait of interest and the number of divisions. We obtain explicit results when the trait is the age or the size, for age and size-controlled models.

Large deviations and fluctuation theorem for selectively decoupled measures on shift spaces

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such decoupling conditions arise naturally in multifractal analysis, in Gibbs states with hard-core interactions, and in the statistics of repeated quantum measurement processes. We also prove the LDP for the entropy production of pairs of such measures and derive the related Fluctuation Relation. The proofs are based on Ruelle–Lanford functions, and the exposition is essentially self-contained.