Resolving entropy contributions in nonequilibrium transitions

Fluids with power-law repulsion: Hyperuniformity and energy fluctuations

We revisit the equilibrium statistical mechanics of a classical fluid of point-like particles with repulsive power-law pair interactions, focusing on density and energy fluctuations at finite temperature. Such long-range interactions, decaying with inter-particle distanceras1/rsinddimensions, are known to fall into two qualitatively different categories. Fors < d('strongly' long-range interactions) there are screening of correlations and suppression of large-wavelength density fluctuations (hyperuniformity). These effects eliminate density modes with arbitrarily large energy. Fors > d('weakly' long-range interactions) screening and hyperuniformity do not occur. Using scaling arguments, variational analysis, and Monte Carlo simulations, we find another qualitative distinction. Fors⩾d/2the strong repulsion at short distances leads to enhanced small-wavelength density fluctuations, decorrelating particle positions. This prevents indefinitely negative entropy and large energy fluctuations. The distinct behaviors fors⩾d/2ands Collapse

Key Words

• Coulombic fluids
• Riesz gas
• entropy
• fluctuations
• hyperuniformity

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Affiliation(s)

H Diamant School of Chemistry and the Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel
E C Oǧuz Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, People's Republic of China

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Universal Relation between Entropy and Kinetics

Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle configurations. It is universal and applicable to steady states arbitrarily far from thermodynamic equilibrium. Applying the general relation to diffusive dynamics yields a relation between the entropy and the (normal or anomalous) diffusion coefficient. The relation can be used to obtain useful bounds for the late-time diffusion coefficient from the calculated steady-state entropy or, conversely, to estimate the entropy based on measured diffusion coefficients. We demonstrate the validity and usefulness of the relation through several examples and discuss its broad range of applications, in particular, for systems far from equilibrium.

Detecting and characterizing phase transitions in active matter using entropy

A major challenge in the study of active matter lies in quantitative characterization of phases and transitions between them. We show how the entropy of a collection of active objects can be used to classify regimes and spatial patterns in their collective behavior. Specifically, we estimate the contributions to the total entropy from correlations between the degrees of freedom of position and orientation. This analysis pin-points the flocking transition in the Vicsek model while clarifying the physical mechanism behind the transition. When applied to experiments on swarming Bacillus subtilis with different cell aspect ratios and overall bacterial area fractions, the entropy analysis reveals a rich phase diagram with transitions between qualitatively different swarm statistics. We discuss physical and biological implications of these findings.