Nonequilibrium fluctuations of chemical reaction networks at criticality: The Schlögl model as paradigmatic case.

Chemical reaction networks can undergo nonequilibrium phase transitions upon variation in external control parameters, such as the chemical potential of a species. We investigate the flux in the associated chemostats that is proportional to the entropy production and its critical fluctuations within the Schlögl model. Numerical simulations show that the corresponding diffusion coefficient diverges at the critical point as a function of system size. In the vicinity of the critical point, the diffusion coefficient follows a scaling form. We develop an analytical approach based on the chemical Langevin equation and van Kampen's system size expansion that yields the corresponding exponents in the monostable regime. In the bistable regime, we rely on a two-state approximation in order to analytically describe the critical behavior.

Coherence of oscillations in the weak-noise limit.

In a noisy environment, oscillations lose their coherence, which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional potential analytically in the weak-noise limit. With this expression, we can prove for this continuum model the analog of an upper bound that has been conjectured for the coherence of oscillations in discrete Markov network models. We show that our approach can also be adapted to motion along a noisy two-dimensional limit cycle. Specifically, we apply our scheme to the noisy Stuart-Landau oscillator and the thermodynamically consistent Brusselator as a simple model for a chemical clock. Our approach thus complements the fairly sophisticated extant general framework based on techniques from Hamilton-Jacobi theory with which we compare our results numerically.

Optimality of nonconservative driving for finite-time processes with discrete states.

An optimal finite-time process drives a given initial distribution to a given final one in a given time at the lowest cost as quantified by total entropy production. We prove that for a system with discrete states this optimal process involves nonconservative driving, i.e., a genuine driving affinity, in contrast to the case of a system with continuous states. In a multicyclic network, the optimal driving affinity is bounded by the number of states within each cycle. If the driving affects forward and backwards rates nonsymmetrically, the bound additionally depends on a structural parameter characterizing this asymmetry.

Nonequilibrium dynamics of isostatic spring networks.

Marginally stable systems exhibit rich critical mechanical behavior. Such isostatic assemblies can be actively driven, but it is unclear how their critical nature affects their nonequilibrium dynamics. Here, we study the influence of isostaticity on the nonequilibrium dynamics of active spring networks. In our model, heterogeneously distributed white or colored, motorlike noise drives the system into a nonequilibrium steady state. We quantify the nonequilibrium dynamics of pairs of network nodes by the characteristic cycling frequency ω-an experimentally accessible measure of the circulation of the associated phase space currents. The distribution of these cycling frequencies exhibits critical scaling, which we approximately capture by a mean-field theory. Finally, we show that the scaling behavior of ω with distance is controlled by a diverging length scale. Overall, we provide a theoretical approach to elucidate the role of marginality in active disordered systems.