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Register a new userAutocorrelation study of the {Theta} transition for a coarse-grained polymer model
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By means of Metropolis Monte Carlo simulations of a coarse-grained model for flexible polymers, we investigate how the integrated autocorrelation times of different energetic and structural quantities depend on the temperature. We show that, due to critical slowing down, an extremal autocorrelation time can also be considered as an indicator for the collapse transition that helps to locate the transition point. This is particularly useful for finite systems, where response quantities such as the specific heat do not necessarily exhibit clear indications for pronounced thermal activity.
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We introduce a coarse-grained deep neural network model (CG-DNN) for liquid water that utilizes 50 rotational and translational invariant coordinates, and is trained exclusively against energies of ~30,000 bulk water configurations. Our CG-DNN potential accurately predicts both the energies and molecular forces of water; within 0.9 meV/molecule and 54 meV/angstrom of a reference (coarse-grained bond-order potential) model. The CG-DNN water model also provides good prediction of several structural, thermodynamic, and temperature dependent properties of liquid water, with values close to that obtained from the reference model. More importantly, CG-DNN captures the well-known density anomaly of liquid water observed in experiments. Our work lays the groundwork for a scheme where existing empirical water models can be utilized to develop fully flexible neural network framework that can subsequently be trained against sparse data from high-fidelity albeit expensive beyond-DFT calculations.
We extend classical coarse-grained entropy, commonly used in many branches of physics, to the quantum realm. We find two coarse-grainings, one using measurements of local particle numbers and then total energy, and the second using local energy measurements, which lead to an entropy that is defined outside of equilibrium, is in accord with the thermodynamic entropy for equilibrium systems, and reaches the thermodynamic entropy in the long-time limit, even in genuinely isolated quantum systems. This answers the long-standing conceptual problem, as to which entropy is relevant for the formulation of the second thermodynamic law in closed quantum systems. This entropy could be in principle measured, especially now that experiments on such systems are becoming feasible.
We consider a model of an extensible semiflexible filament moving in two dimensions on a motility assay of motor proteins represented explicitly as active harmonic linkers. Their heads bind stochastically to polymer segments within a capture radius, and extend along the filament in a directed fashion before detaching. Both the extension and detachment rates are load-dependent and generate an active drive on the filament. The filament undergoes a first order phase transition from open chain to spiral conformations and shows a reentrant behavior in both the active extension and the turnover, defined as the ratio of attachment-detachment rates. Associated with the phase transition, the size and shape of the polymer changes non-monotonically, and the relevant autocorrelation functions display double-exponential decay. The corresponding correlation times show a maximum signifying the dominance of spirals. The orientational dynamics captures the rotation of spirals, and its correlation time decays with activity as a power law.
Water modeling is a challenging problem. Its anomalies are difficult to reproduce, promoting the proliferation of a large number of computational models, among which researchers select the most appropriate for the property they study. In this chapter, we introduce a coarse-grained model introduced by Franzese and Stanley (FS) that accounts for the many-body interactions of water. We review mean-field calculations and Monte Carlo simulations on water monolayers for a wide range of pressures and temperatures, including extreme conditions. The results show the presence of two dynamic crossovers and explain the origin of diffusion anomalies. Moreover, the model shows that all the different scenarios, proposed in the last decades as alternative explanations of the experimental anomalies of water, can be related by the fine-tuning of the many-body (cooperative) interaction. Once this parameter is set from the experiments, the FS model predicts a phase transition between two liquids with different densities and energies in the supercooled water region, ending in a liquid-liquid critical point. From this critical point stems a liquid-liquid Widom line, i.e., the locus of maxima of the water correlation length, that in the FS model can be directly calculated. The results are consistent with the extrapolations from experiments. Furthermore, they agree with those from atomistic models but make predictions over a much wider thermodynamic region, allowing for a better interpretation of the available experimental data. All these findings provide a coherent picture of the properties of water and confirm the validity of the FS model that has proved to be useful for large-scale simulations of biological systems.
We investigate the detailed properties of Observational entropy, introduced by v{S}afr{a}nek et al. [Phys. Rev. A 99, 010101 (2019)] as a generalization of Boltzmann entropy to quantum mechanics. This quantity can involve multiple coarse-grainings, even those that do not commute with each other, without losing any of its properties. It is well-defined out of equilibrium, and for some coarse-grainings it generically rises to the correct thermodynamic value even in a genuinely isolated quantum system. The quantity contains several other entropy definitions as special cases, it has interesting information-theoretic interpretations, and mathematical properties -- such as extensivity and upper and lower bounds -- suitable for an entropy. Here we describe and provide proofs for many of its properties, discuss its interpretation and connection to other quantities, and provide numerous simulations and analytic arguments supporting the claims of its relationship to thermodynamic entropy. This quantity may thus provide a clear and well-defined foundation on which to build a satisfactory understanding of the second thermodynamical law in quantum mechanics.
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