1,720,997 research outputs found
Entropy production in non-equilibrium systems
Full text linkIn questa tesi studiamo la produzione di entropia in sistemi fuori dall'equilibrio. Nella prima parte ci concentriamo su sistemi con un numero finito di stati, vicini all'equilibrio termodinamico, che possono essere descritti da una Master Equation. Per sistemi di questo tipo è possibile mappare la dinamica in una rete di stati, rappresentati da nodi, collegati da rate di transizione, identificati da links. In questo contesto, analizziamo la produzione di entropia di ensemble di reti generate casualmente con vincoli specifici, ad esempio la taglia del sistema, e identifichiamo i parametri più importanti che ne determinano il valore. Questa analisi fornisce una stima per la produzione di entropia basata che può essere utilizzata come punto di partenza per il confronto con particolari sistemi di interesse. Nella seconda parte della tesi esaminiamo come il coarse-graining influenzi la nostra capacità di stimare alcune proprietà fisiche di un sistema. Per sistemi fuori dall’equilibrio descritti da una Master Equation, la produzione di entropia può essere stimata utilizzando la formula di Schnakenberg. D'altra parte, alcuni anni fa Seifert ha derivato una formula analoga per sistemi descritti da una Fokker-Planck Equation. In questa tesi miriamo a creare un ponte fra queste due formulazioni e, partendo da un sistema con un numero finito di stati calcoliamo come la produzione di entropia di Schnakenberg sia influenzata dalla procedura di coarse-graining. Mostriamo che tale valore può essere ridotto alla formula di Seifert per alcune scelte particolari della dinamica, ma che, abbastanza sorprendentemente, in generale i flussi microscopici presenti nel sistema danno un contributo macroscopico non negativo alla produzione di entropia. Di conseguenza, trascurare alcune informazioni porta a sottostimare la produzione di entropia, e solo un limite inferiore può essere fornito quando la dinamica è coarse-grained. Infine, nell’ultima sezione della tesi, studiamo somiglianze e differenze tra stati stazionari di non equilibrio e driving periodico in sistemi diffusivi. Un sistema che viola il bilancio dettagliato evolve asintoticamente in uno stato stazionario, che non è uno stato di equilibrio poiché presenta correnti non nulle. Analogamente, quando il bilancio dettagliato è presente in ogni istante di tempo, ma il sistema subisce variazioni periodiche dei parametri esterni, quest’ultimo evolve verso uno stato periodico in cui sono presenti correnti non nulle. In entrambi i casi il costo per produrre tali correnti in tutto il sistema è rappresentato dalla produzione di entropia. In questa tesi miriamo a confrontare questi due scenari per un sistema diffusivo continuo monodimensionale con condizioni al contorno periodiche, descritto da un'equazione di Fokker-Planck, che è il modo più naturale per analizzare le macchine molecolari. Innanzitutto, mostriamo che la produzione di entropia non è equivalente in questi due scenari: il rate di produzione di entropia in un sistema con driving periodico è sempre maggiore del rate di produzione di entropia in un sistema stazionario senza bilancio dettagliato, quando entrambi producono la stessa corrente e hanno la stessa distribuzione di probabilità (mediata nel tempo). Successivamente, mostriamo come costruire sia uno stato stazionario di non equilibrio sia un protocollo di variazione periodica dei parametri esterni che producano una data probabilità (mediata nel tempo) e una data corrente
Information-driven transitions in projections of underdamped dynamics
No full textLow-dimensional representations of underdamped systems often provide useful insights and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most information on observed spatial trajectories. We show that, in paradigmatic systems, the minimization of the information loss drives the appearance of a discontinuous transition in the optimal model parameters. Our results raise serious warnings for general inference approaches, and they unravel fundamental properties of effective dynamical representations impacting several fields, from biophysics to dimensionality reduction
Turing patterns in multiplex networks
Full text linkThe 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/
Mutual information in changing environments: Nonlinear interactions, out-of-equilibrium systems, and continuously varying diffusivities
No full textBiochemistry, ecology, and neuroscience are examples of prominent fields aiming at describing interacting systems that exhibit nontrivial couplings to complex, ever-changing environments. We have recently shown that linear interactions and a switching environment are encoded separately in the mutual information of the overall system. Here we first generalize these findings to a broad class of nonlinear interacting models. We find that a new term in the mutual information appears, quantifying the interplay between nonlinear interactions and environmental changes, and leading to either constructive or destructive information interference. Furthermore, we show that a higher mutual information emerges in out-of-equilibrium environments with respect to an equilibrium scenario. Finally, we generalize our framework to the case of continuously varying environments. We find that environmental changes can be mapped exactly into an effective spatially varying diffusion coefficient, shedding light on modeling of biophysical systems in inhomogeneous media.LB
Coarse-grained entropy production with multiple reservoirs: Unraveling the role of time scales and detailed balance in biology-inspired systems
Full text linkA 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
Excitation-Inhibition Balance Controls Information Encoding in Neural Populations
No full text: Understanding how the complex connectivity structure of the brain shapes its information-processing capabilities is a long-standing question. By focusing on a paradigmatic architecture, we study how the neural activity of excitatory and inhibitory populations encodes information on external signals. We show that at long times information is maximized at the edge of stability, where inhibition balances excitation, both in linear and nonlinear regimes. In the presence of multiple external signals, this maximum corresponds to the entropy of the input dynamics. By analyzing the case of a prolonged stimulus, we find that stronger inhibition is instead needed to maximize the instantaneous sensitivity, revealing an intrinsic tradeoff between short-time responses and long-time accuracy. In agreement with recent experimental findings, our results pave the way for a deeper information-theoretic understanding of how the balance between excitation and inhibition controls optimal information-processing in neural populations
Fluctuations of entropy production of a run-and-tumble particle
Full text linkOut-of-equilibrium systems continuously generate entropy, with its rate of production being a fingerprint of nonequilibrium conditions. In small-scale dissipative systems subject to thermal noise, fluctuations of entropy production are significant. Hitherto, mean and variance have been abundantly studied, even if higher moments might be important to fully characterize the system of interest. Here, we introduce a graphical method to compute any moment of entropy production for a generic discrete-state system. Then, we focus on a paradigmatic model of active particles, i.e., run-and-tumble dynamics, which resembles the motion observed in several micro-organisms. Employing our framework, we compute the first three cumulants of the entropy production for a discrete version of this model. We also compare our analytical results with numerical simulations. We find that as the number of states increases, the distribution of entropy production deviates from a Gaussian. Finally, we extend our framework to a continuous state-space run-and-tumble model, using an appropriate scaling of the transition rates. The approach presented here might help uncover the features of nonequilibrium fluctuations of any current in biological systems operating out-of-equilibrium.LB
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
Full text linkThe 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
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