16 research outputs found
Coarse-grained entropy production with multiple reservoirs: Unraveling the role of time scales and detailed balance in biology-inspired systems
No full textA general framework to describe a vast majority of biology-inspired systems is to model them as stochastic processes in which multiple couplings are in play at the same time. Molecular motors, chemical reaction networks, catalytic enzymes, and particles exchanging heat with different baths, constitute some interesting examples of such a modelization. Moreover, they usually operate out of equilibrium, being characterized by a net production of entropy, which entails a constrained efficiency. Hitherto, in order to investigate multiple processes simultaneously driving a system, all theoretical approaches deal with them independently, at a coarse-grained level, or employing a separation of time scales. Here, we explicitly take in consideration the interplay among time scales of different processes and whether or not their own evolution eventually relaxes toward an equilibrium state in a given subspace. We propose a general framework for multiple coupling, from which the well-known formulas for the entropy production can be derived, depending on the available information about each single process. Furthermore, when one of the processes does not equilibrate in its subspace, even if much faster than all the others, it introduces a finite correction to the entropy production. We employ our framework in various simple and pedagogical examples, for which such a corrective term can be related to a typical scaling of physical quantities in play.LB
Mutual Information Disentangles Interactions from Changing Environments
No full textReal-world systems are characterized by complex interactions of their internal degrees of freedom, while living in ever-changing environments whose net effect is to act as additional couplings. Here, we introduce a paradigmatic interacting model in a switching, but unobserved, environment. We show that the limiting properties of the mutual information of the system allow for a disentangling of these two sources of couplings. Further, our approach might stand as a general method to discriminate complex internal interactions from equally complex changing environments.LB
Pattern formation for reactive species undergoing anisotropic diffusion
No full textTuring instabilities for a two species reaction-diffusion systems is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive. Under this working hypothesis, the conditions for the onset of the instability are mathematically derived and numerically validated. Patterns which closely resemble those obtained in the classical context of isotropic diffusion, develop when the usual Turing condition is violated, along one of the two accessible directions of migration. Remarkably, theinstability can also set in when the activator diffuses faster than the inhibitor, along the direction for which the usual Turing conditions are not matche
Turing patterns in multiplex networks
No full textThe theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled. The interaction between adjacent layers can seed the instability of an homogeneous fixed point, yielding self-organized patterns which are instead impeded in the limit of decoupled layers. Patterns on individual layers can also fade away due to cross-talking between layers. Analytical results are compared to direct simulations.<br/
Powerful ordered collective heat engines
No full textWe introduce a class of stochastic engines in which the regime of units operating synchronously can boost the performance. Our approach encompasses a minimal setup composed of N interacting units placed in contact with two thermal baths and subjected to a constant driving worksource. The interplay between unit synchronization and interaction leads to an efficiency at maximum power between the Carnot η_c and the Curzon-Ahlborn bound η_CA. Moreover, these limits can be respectively saturated maximizing the efficiency, and by simultaneous optimization of power and efficiency. We show that the interplay between Ising-like interactions and a collective ordered regime is crucial to operate as a heat engine. The main system features are investigated by means of a linear analysis near equilibrium, and developing an effective discrete-state model that captures the effects of the synchronous phase. The robustness of our findings extends beyond the all-to-all interactions and paves the way for the building of promising nonequilibrium thermal machines based on ordered structures
Turing instabilities on Cartesian product networks
No full textThe problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the individual networks that build the Cartesian product. The dispersion relation which controls the onset of the instability depends on a set of discrete wavelengths, the eigenvalues of the aforementioned Laplacians. Patterns can develop on the Cartesian network, if they are supported on at least one of its constitutive sub-graphs. Multiplex networks are also obtained under specific prescriptions. In this case, the criteria for the instability reduce to compact explicit formulae. Numerical simulations carried out for the Mimura-Murray reaction kinetics confirm the adequacy of the proposed theory
Explorability and the origin of network sparsity in living systems
No full textThe increasing volume of ecologically and biologically relevant data has revealed a wide collection of emergent patterns in living systems. Analysing different data sets, ranging from metabolic gene-regulatory to species interaction networks, we find that these networks are sparse, i.e. the percentage of the active interactions scales inversely proportional to the system size. To explain the origin of this puzzling common characteristic, we introduce the new concept of explorability: a measure of the ability of an interacting system to adapt to newly intervening changes. We show that sparsity is an emergent property resulting from optimising both explorability and dynamical robustness, i.e. the capacity of the system to remain stable after perturbations of the underlying dynamics. Networks with higher connectivities lead to an incremental difficulty to find better values for both the explorability and dynamical robustness, associated with the fine-tuning of the newly added interactions. A relevant characteristic of our solution is its scale invariance, i.e., it remains optimal when several communities are assembled together. Connectivity is also a key ingredient in determining ecosystem stability and our proposed solution contributes to solving May's celebrated complexity-stability paradox
Thermodynamics and kinetics of protonated merocyanine photoacids in water
No full textMetastable-state photoacids (mPAHs) are chemical species whose photo-activated state is long-lived enough to allow for proton diffusion. Liao's photoacid (1) represents the archetype of mPAHs, and is being widely used on account of its unique capability to change the acidity of aqueous solutions reversibly. The behavior of 1 in water, however, still remains poorly understood. Herein, we provide in-depth insights on the thermodynamics and kinetics of 1 in water through a series of comparative 1H NMR and UV-Vis studies and relative modelling. Under dark conditions, we quantified a three-component equilibrium system where the dissociation (Ka) of the open protonated form (MCH) is followed by isomerization (Kc) of the open deprotonated form (MC) to the closed spiropyran form (SP)-i.e., in the absence of light, the ground state acidity can be expressed as KGSa = Ka(1 + Kc). On the other hand, under powerful and continuous light irradiation we were able to assess, for the first time experimentally, the dissociation constant (KMSa) of the protonated metastable state (cis-MCH). In addition, we found that thermal ring-opening of SP is always rate-determining regardless of pH, whereas hydrolysis is reminiscent of what is found for Schiff bases. The proposed methodology is general, and it was applied to two other compounds bearing a shorter (ethyl, 2) and a longer (butyl, 3) alkyl-1-sulfonate bridge. We found that the pKa remains constant, whereas both pKc and pKMSa linearly increase with the length of the alkyl bridge. Importantly, all results are consistent with a four-component model cycle, which describes perfectly the full dynamics of proton release/uptake of 1-3 in water. The superior hydrolytic stability and water solubility of compound 3, together with its relatively high pKGSa (low Kc), allowed us to achieve fully reversible jumps of 2.5 pH units over 18 consecutive cycles (6 hours). This journal i
Tighter thermodynamic bound on the speed limit in systems with unidirectional transitions
No full textWe consider a general discrete state-space system with both unidirectional and bidirectional links. In contrast to bidirectional links, there is no reverse transition along the unidirectional links Herein, we first compute the statistical length and the thermodynamic cost function for transitions in the probability space, highlighting contributions from total, environmental, and resetting (unidirectional) entropy production. Then we derive the thermodynamic bound on the speed limit to connect two distributions separated by a finite time, showing the effect of the presence of unidirectional transitions. Uncertainty relationships can be found for the temporal first and second moments of the average resetting entropy production. We derive simple expressions in the limit of slow unidirectional transition rates. Finally, we present a refinement of the thermodynamic bound by means of an optimization procedure. We numerically investigate these results on systems that stochastically reset with constant and periodic resetting rate.LB
