9 results found
Alston H, Cocconi L, Bertrand T, 2022, Non-equilibrium thermodynamics of diffusion in fluctuating potentials, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 55, ISSN: 1751-8113
Cocconi L, Salbreux G, Pruessner G, 2022, Scaling of entropy production under coarse graining in active disordered media, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, Vol: 105, ISSN: 1539-3755
Entropy production plays a fundamental role in the study of non-equilibriumsystems by offering a quantitative handle on the degree of time-reversalsymmetry breaking. It depends crucially on the degree of freedom considered aswell as on the scale of description. It was hitherto unknown how the entropyproduction at one resolution of the degrees of freedom is related to theentropy production at another resolution. This relationship is of particularrelevance to coarse grained and continuum descriptions of a given phenomenon.In this work, we derive the scaling of the entropy production under iterativecoarse graining on the basis of the correlations of the underlying microscopictransition rates. Our approach unveils a natural criterion to distinguishequilibrium-like and genuinely non-equilibrium macroscopic phenomena based onthe sign of the scaling exponent of the entropy production per mesostate.
Cocconi L, Kuhn-Regnier A, Neuss M, et al., 2021, Reconstructing the Intrinsic Statistical Properties of Intermittent Locomotion Through Corrections for Boundary Effects, BULLETIN OF MATHEMATICAL BIOLOGY, Vol: 83, ISSN: 0092-8240
Christensen K, Cocconi L, Sendova-Franks AB, 2021, Animal intermittent locomotion: a null model for the probability of moving forward in bounded space., Journal of Theoretical Biology, Vol: 510, Pages: 1-19, ISSN: 0022-5193
We present a null model to be compared with biological data to test for intrinsic persistence in movement between stops during intermittent locomotion in bounded space with different geometries and boundary conditions. We describe spatio-temporal properties of the sequence of stopping points r1,r2,r3,… visited by a Random Walker within a bounded space. The path between stopping points is not considered, only the displacement. Since there are no intrinsic correlations in the displacements between stopping points, there is no intrinsic persistence in the movement between them. Hence, this represents a null-model against which to compare empirical data for directional persistence in the movement between stopping points when there is external bias due to the bounded space. This comparison is a necessary first step in testing hypotheses about the function of the stops that punctuate intermittent locomotion in diverse organisms. We investigate the probability of forward movement, defined as a deviation of less than 90° between two successive displacement vectors, as a function of the ratio between the largest displacement between stops that could be performed by the random walker and the system size, α=Δℓ/Lmax. As expected, the probability of forward movement is 1/2 when α→0. However, when α is finite, this probability is less than 1/2 with a minimum value when α=1. For certain boundary conditions, the minimum value is between 1/3 and 1/4 in 1D while it can be even lower in 2D. The probability of forward movement in 1D is calculated exactly for all values 0<α⩽1 for several boundary conditions. Analytical calculations for the probability of forward movement are performed in 2D for circular and square bounded regions with one boundary condition. Numerical results for all values 0<α⩽1 are presented for several boundary conditions. The cases of rectangle and ellipse are also considered and an approximate model of
Cocconi L, de Gennes M, Salbreux G, 2021, Strip it out and build it back! Engineering a morphogen gradient, TheScienceBreaker, Vol: 07
Cocconi L, Garcia Millan R, Zhen Z, et al., 2020, Entropy production in exactly solvable systems, Entropy: international and interdisciplinary journal of entropy and information studies, Vol: 22, Pages: 1-33, ISSN: 1099-4300
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms.
Kuhn-Regnier A, Cocconi L, Neuss M, 2020, bounded-rand-walkers
This is the first release of the software used in our paper investigating bounded random walks.We implemented an adaptive rejection sampling algorithm in both Python and C++, allowing the investigation of bounded random walks given user-specified intrinsic step distributions and convex geometries. Multiple binning techniques are used throughout in order to enable analysis of both 2D gridded and 1D radially-averaged data, and a custom integrator is used to achieve high numerical accuracy where needed.
Stapornwongkul KS, de Gennes M, Cocconi L, et al., 2020, Patterning and growth control in vivo by an engineered GFP gradient, SCIENCE, Vol: 370, Pages: 321-+, ISSN: 0036-8075
Among observables characterizing the random exploration of a graph or lattice, the cover time, namely, the time to visit every site, continues to attract widespread interest. Much insight about cover times is gained by mapping to the (spaceless) coupon collector problem, which amounts to ignoring spatiotemporal correlations, and an early conjecture that the limiting cover time distribution of regular random walks on large lattices converges to the Gumbel distribution in d≥3 was recently proved rigorously. Furthermore, a number of mathematical and numerical studies point to the robustness of the Gumbel universality to modifications of the spatial features of the random search processes (e.g., introducing persistence and/or intermittence, or changing the graph topology). Here we investigate the robustness of the Gumbel universality to dynamical modification of the temporal features of the search, specifically by allowing the random walker to “accelerate” or “decelerate” upon visiting a previously unexplored site. We generalize the mapping mentioned above by relating the statistics of cover times to the roughness of 1/fα Gaussian signals, leading to the conjecture that the Gumbel distribution is but one of a family of cover time distributions, ranging from Gaussian for highly accelerated cover, to exponential for highly decelerated cover. While our conjecture is confirmed by systematic Monte Carlo simulations in dimensions d>3, our results for acceleration in d=3 challenge the current understanding of the role of correlations in the cover time problem.
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