Boltzmann's H-function for molecules with orientational degrees of freedom: Emergence of unique features

Kumar, S and Bagchi, B (2024) Boltzmann's H-function for molecules with orientational degrees of freedom: Emergence of unique features. In: Journal of Chemical Physics, 161 (6).

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Abstract

Boltzmann�s H-function H(t), often regarded as an analog of time-dependent entropy, holds a venerable place in the history of science. However, accurate numerical evaluation of H(t) for particles other than atoms is rare. To remove this lacuna, we generalize Boltzmann�s H-function to a gas of molecules with orientational degrees of freedom and evaluate H(t) from the time-dependent joint probability distribution function f(p, L, t) for linear (p) and angular (L) momenta, evolving from an initial nonequilibrium state, by molecular dynamics simulations. We consider both prolate- and oblate-shaped particles, interacting via the well-known Gay-Berne potential and obtain the relaxation of the generalized molecular H(t) from initial (t = 0) nonequilibrium states. In the long-time limit, the H function saturates to its exact equilibrium value, which is the sum of translational and rotational contributions to the respective entropies. Both the translational and rotational components of H(t) decay nearly exponentially with time; the rotational component is more sensitive to the molecular shape that enters through the aspect ratio. A remarkable rapid decrease in the rotational relaxation time is observed as the spherical limit is approached, in a way tantalizingly reminiscent of Hu-Zwanzig hydrodynamic prediction with the slip boundary condition. In addition, we obtain H(t) analytically by solving the appropriate translational and rotational Fokker-Planck equation and obtain a modest agreement with simulations. We observe a remarkable signature of translation-rotation coupling as a function of molecular shape, captured through a physically meaningful differential term that quantifies the magnitude of translation-rotation coupling. © 2024 Author(s).

Item Type:	Journal Article
Publication:	Journal of Chemical Physics
Publisher:	American Institute of Physics
Additional Information:	The copyright for this article belongs to the publisher.
Keywords:	Angular distribution; Boltzmann equation; Fokker Planck equation; Molecular docking; Probability density function, 'lacuna'; Boltzmann; H function; History of science; Molecular shapes; Nonequilibrium state; Rotational component; Time dependent; Time-dependent entropy; Unique features, Aspect ratio, phosmet, article; atom; controlled study; degree of freedom; entropy; human; hydrodynamics; molecular dynamics; prediction; probability; relaxation time; rotation; simulation
Department/Centre:	Division of Chemical Sciences > Solid State & Structural Chemistry Unit
Date Deposited:	29 Aug 2024 06:04
Last Modified:	29 Aug 2024 06:04
URI:	http://eprints.iisc.ac.in/id/eprint/85969

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