Publicación: The role of thermal fluctuations in the motion of a free body
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2024
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info:eu-repo/semantics/openAccess
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Resumen
The motion of a rigid body is described in Classical Mechanics with the venerable Euler’s equations which are based on the assumption that the relative distances among the constituent particles are fixed in time. Real bodies, however, cannot satisfy this property, as a consequence of thermal fluctuations. We generalize Euler’s equations for a free body in order to describe dissipative and thermal fluctuation effects in a thermodynamically consistent way. The origin of these effects is internal, i.e. not due to an external thermal bath. The stochastic differential equations governing the orientation and central moments of the body are derived from first principles through the theory of coarse-graining. Within this theory, Euler’s equations emerge as the reversible part of the dynamics. For the irreversible part, we identify two distinct dissipative mechanisms; one associated with diffusion of the orientation, whose origin lies in the difference between the spin velocity and the angular velocity, and one associated with the damping of dilations, i.e. inelasticity. We show that a deformable body with zero angular momentum will explore uniformly, through thermal fluctuations, all possible orientations. When the body spins, the equations describe the evolution towards the alignment of the body’s major principal axis with the angular momentum vector. In this alignment process, the body increases its temperature. We demonstrate that the origin of the alignment process is not inelasticity but rather orientational diffusion. The theory also predicts the equilibrium shape of a spinning body.
Descripción
The registered version of this article, first published in “European Journal of Mechanics - A/Solids, Volume 103", is available online at the publisher's website: Elsevier, https://doi.org/10.1016/j.euromechsol.2023.105184
La versión registrada de este artículo, publicado por primera vez en “European Journal of Mechanics - A/Solids, Volume 103", está disponible en línea en el sitio web del editor: Elsevier, https://doi.org/10.1016/j.euromechsol.2023.105184
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Palabras clave
Quasi-rigid bodies, Statistical mechanics, Coarse-graining, Thermal fluctuations, Euler’s equations
Citación
Pep Español, Mark Thachuk, J.A. de la Torre, The role of thermal fluctuations in the motion of a free body, European Journal of Mechanics - A/Solids, Volume 103, 2024, 105184, ISSN 0997-7538, https://doi.org/10.1016/j.euromechsol.2023.105184
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Facultades y escuelas::Facultad de Ciencias
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