Full statistics of conjugated thermodynamic ensembles in chains of bistable units

Manon Benedito (1, 2) , Fabio Manca (3) , Stefano Giordano (1, 2)

1 IEMN - Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520
2 AIMAN-FILMS - IEMN - Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN
3 LPS - Laboratoire de Physique Statistique de l'ENS

The statistical mechanics and the thermodynamics of small systems are characterized by 1 the non-equivalence of the statistical ensembles. Concerning a polymer chain or an arbitrary chain 2 of independent units, this concept leads to different force-extension responses for the isotensional 3 (Gibbs) and the isometric (Helmholtz) thermodynamic ensembles for a limited number of units 4 (far from the thermodynamic limit). While the average force-extension response has been largely 5 investigated in both Gibbs and Helmholtz ensembles, the full statistical characterization of this 6 thermo-mechanical behavior has not been approached by evaluating the corresponding probability 7 densities. Therefore, we elaborate in this paper a technique for obtaining the probability density of the 8 extension when the force is applied (Gibbs ensemble) and the probability density of the force when the 9 extension is prescribed (Helmholtz ensemble). This methodology, here developed at thermodynamic 10 equilibrium, is applied to a specific chain composed of units characterized by a bistable potential 11 energy, which is able to mimic the folding and unfolding of several macromolecules of biological 12 origin. 13

Mots clés: small systems thermodynamics; Gibbs and Helmholtz ensembles; polymer chain; bistability; ensembles equivalence

Domaines: Physique [physics]; Science non linéaire [physics]; Mécanique [physics]

Manon Benedito, Fabio Manca, Stefano Giordano. Full statistics of conjugated thermodynamic ensembles in chains of bistable units. Inventions, 2019, 4 (1), pp.19. ⟨10.3390/inventions4010019⟩. ⟨hal-02337961⟩