1,721,094 research outputs found
Effective equations in complex systems: From Langevin to machine learning
No full textThe problem of effective equations is reviewed and discussed. Starting from the classical Langevin equation, we show how it can be generalized to Hamiltonian systems with non-standard kinetic terms. A numerical method for inferring effective equations from data is discussed; this protocol allows to check the validity of our results. In addition we show that, with a suitable treatment of time series, such protocol can be used to infer effective models from experimental data. We briefly discuss the practical and conceptual difficulties of a pure data-driven approach in the building of models
Effective equations for reaction coordinates in polymer transport
No full textIn the framework of the problem of finding proper reaction coordinates (RCs) for complex systems and their effective evolution equations, we consider the case study of a polymer chain in an external double-well potential, experiencing thermally activated dynamics. Langevin effective equations describing the macroscopic dynamics of the system can be inferred from data by using a data-driven approach, once a suitable set of RCs is chosen. We show that, in this case, the validity of such choice depends on the stiffness of the polymer's bonds: if they are sufficiently rigid, we can employ a reduced description based only on the coordinate of the center of mass; whereas, if the stiffness reduces, the one-variable dynamics is no more Markovian and (at least) a second reaction coordinate has to be taken into account to achieve a realistic dynamical description in terms of memoryless Langevin equations
About the role of chaos and coarse graining in statistical mechanics
No full textWe discuss the role of ergodicity and chaos for the validity of statistical laws. In particular we explore the basic aspects of chaotic systems (with emphasis on the finite-resolution) on systems composed of a huge number of particles
Correlation functions and relaxation properties in chaotic dynamics and statistical mechanics
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Relevance of initial and final conditions for the fluctuation relation in Markov processes
No full textA Markovian approach to the Prandtl–Tomlinson frictional model
No full textWe consider the Prandtl–Tomlinson model in the case of a constant driving force and in the presence of thermal fluctuations. We show that the system dynamics is well reproduced by a simplified description obtained through a Markov process, even in the case of potentials with several minima. After estimating the chain parameters by numerical simulation, we compute the average velocity and friction at varying driving force and temperature. Then we take advantage of this approach for calculating the entropy produced by the system and, in the case of a single minimum potential, to derive its explicit relation with the external force and the mobility at low temperatures. We observe that the coefficient relating the entropy production to the force is not a monotonic function of the temperature
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