Study of entropy-diffusion relation in deterministic Hamiltonian systems through microscopic analysis

Acharya, S and Bagchi, B (2020) Study of entropy-diffusion relation in deterministic Hamiltonian systems through microscopic analysis. In: Journal of Chemical Physics, 153 (18).

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Abstract

Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study and any derivation of an algebraic relation between the two do not seem to exist. Here, we explore the nature of this entropy-diffusion relation in three deterministic systems where an accurate estimate of both can be carried out. We study three deterministic model systems: (a) the motion of a single point particle with constant energy in a two-dimensional periodic potential energy landscape, (b) the same in the regular Lorentz gas where a point particle with constant energy moves between collisions with hard disk scatterers, and (c) the motion of a point particle among the boxes with small apertures. These models exhibit diffusive motion in the limit where ergodicity is shown to exist. We estimate the self-diffusion coefficient of the particle by employing computer simulations and entropy by quadrature methods using Boltzmann's formula. We observe an interesting crossover in the diffusion-entropy relation in some specific regions, which is attributed to the emergence of correlated returns. The crossover could herald a breakdown of the Rosenfeld-like exponential scaling between the two, as observed at low temperatures. Later, we modify the exponential relation to account for the correlated motions and present a detailed analysis of the dynamical entropy obtained via the Lyapunov exponent, which is rather an important quantity in the study of deterministic systems. © 2020 Author(s).

Item Type:	Journal Article
Publication:	Journal of Chemical Physics
Publisher:	American Institute of Physics Inc.
Additional Information:	The copyright of this article belongs to American Institute of Physics Inc.
Keywords:	Diffusion in liquids; Entropy; Lyapunov methods; Potential energy, Algebraic relations; Deterministic modeling; Deterministic systems; Exponential relation; Hamiltonian systems; Microscopic analysis; Periodic potentials; Self-diffusion coefficients, Hamiltonians, article; computer simulation; diffusion coefficient; entropy; low temperature; motion
Department/Centre:	Division of Chemical Sciences > Solid State & Structural Chemistry Unit
Date Deposited:	02 Feb 2021 11:37
Last Modified:	02 Feb 2021 11:37
URI:	http://eprints.iisc.ac.in/id/eprint/67303

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