From Action Principle to Stochastic Thermodynamics of Elastic and Viscous Active Matter
Abstract
Motivated by the complex material properties of living matter, we derive a framework of stochastic thermo- and elastodynamics for active materials from the classical principle of least action and the Rayleighian formalism for external forces. Our approach couples the local barycentric collective coordinate and the streaming velocity as the canonical conjugate pair, which unifies various descriptions of elastic and viscous soft matter, including Helfrich theory for lipid membranes, linear and nonlinear elasticity of thin shells and deformable droplets, as well as hydrodynamics of active and passive fluids. The Lagrangian mechanics of collective field variables permits direct applications of the results and theorems from statistical mechanics to existing models of complex soft and living matter. To illustrate the potential applications of stochastic elastodynamics in biology, we derive and simulate a boundary-driven deformation model of an elastic cell nucleus in the presence of fluctuations.
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BibTeX
@misc{barletta2026from,
title = {{From Action Principle to Stochastic Thermodynamics of Elastic and Viscous Active Matter}},
author = {Valentina Barletta and Michele Lupini and Ian D. Estabrook and Laeschkir Würthner and Isabella R. Graf and Caren Norden and Lamberto Rondoni and Anna Erzberger and Roman Belousov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21835},
eprint = {2610.21835},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21835},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Action Principle to Stochastic Thermodynamics of Elastic and Viscous Active Matter
AU - Valentina Barletta
AU - Michele Lupini
AU - Ian D. Estabrook
AU - Laeschkir Würthner
AU - Isabella R. Graf
AU - Caren Norden
AU - Lamberto Rondoni
AU - Anna Erzberger
AU - Roman Belousov
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.21835
UR - https://arxiv.org/abs/2610.21835
AB - Motivated by the complex material properties of living matter, we derive a framework of stochastic thermo- and elastodynamics for active materials from the classical principle of least action and the Rayleighian formalism for external forces. Our approach couples the local barycentric collective coordinate and the streaming velocity as the canonical conjugate pair, which unifies various descriptions of elastic and viscous soft matter, including Helfrich theory for lipid membranes, linear and nonlinear elasticity of thin shells and deformable droplets, as well as hydrodynamics of active and passive fluids. The Lagrangian mechanics of collective field variables permits direct applications of the results and theorems from statistical mechanics to existing models of complex soft and living matter. To illustrate the potential applications of stochastic elastodynamics in biology, we derive and simulate a boundary-driven deformation model of an elastic cell nucleus in the presence of fluctuations.
ER -