EXTREMAL PRINCIPLES IN NON-EQUILIBRIUM THERMODYNAMICS (A NATURE INSPIRATION) - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2021

EXTREMAL PRINCIPLES IN NON-EQUILIBRIUM THERMODYNAMICS (A NATURE INSPIRATION)

Résumé

Along the years, a number of researchers have used variational principles to derive important results in thermodynamics for studying the general evolution of systems. In this contribution, we clarify the two entropy production extremisation principles and analyse their relation with the least-action principle and fastest dissipation principle. Two of the most famous variational principles in non-equilibrium thermodynamics are Ziegler’s maximization of entropy production (MaxEP) and Prigogine’s minimization of entropy production (MinEP). Despite their apparent incompatibility, both principles coexist together. According to Martyushev, “If the time is short, the system maximizes entropy production at preset fixed forces at a given moment… If the time is long, the system changes free thermodynamic forces so as to decrease entropy production”.1 Consider flux-force couples {J,X} like {heat flux, 1/T gradient} {i comp. diffusion flux, -μ_i/T gradient} {chemical reaction, -∑▒υ_i μ_i/T gradient}. The usage is to write transport laws as single linear relations flux and force, like Fourier’s or Fick’s law, but Onsager’s linear non-equilibrium thermodynamics proves a more general multilinear expression J_i=∑_j▒〖L_ij X_j 〗 . Then, Ziegler’s MaxEP states that fluxes J associated to forces X maximize the entropy production σ of the system under strict assumptions: (i) σ is a function of fluxes, σ_a≡σ(▁J); (ii) σ equals the sum of fluxes times forces in the system,σ_b≡σ=▁J.▁X. With 2 forces X_1,X_2 and 2 fluxes J_1,J_2 only in the system, Ziegler’s principle is easily represented with the 3-D coordinates J_1,J_2,σ (see Figure). Assumption (i) is displayed by a surface (orange), and assumption (ii) is a plane (blue). Generally their intersection is a curve, and MaxEP postulates that the exact state of the system corresponds to the maximum of this curve with respect to coordinate σ. MinEP principle states that, if a number of forces X_1,X_2,…,X_k is fixed and the rest of the forces X_(k+1),X_(k+2),…,X_n is free to vary, then the system evolves in such a way that it reaches a minimum of entropy production at the steady state. In the figure, when X_1 is fixed, the change in the free force X_2 corresponds to a rotation of the plane σ_b=▁J.▁X. The stationary state J_2=0 corresponds to a minimum of entropy production, as depicted by the red dot in the figure. This allows us to refine Martyushev’s statement, saying that the system maximizes entropy production at every instant, but its evolution in time decreases entropy production. Some common conjectures in non-equilibrium thermodynamics claim that this evolution follows a least-action principle or a fastest dissipation principle.2 However, these conjectures are mostly stated vaguely and without a consensus in academia. Here, we investigate whether the least-action principle refers to: 1) minimizing the arc length of a trajectory between an initial and a stationary point on the surface σ_a; or 2) minimizing the amount of entropy produced during this evolution. We also question whether the fastest dissipation principle refers to minimizing the time necessary for a system to go from an initial state to a stationary state. These conjectures are tested for a near-equilibrium system with 2 coupled reactions.
Abstract - ESAT - da Cunha et al.pdf (670.7 Ko) Télécharger le fichier
extremum_principles_Gerbaud_ESAT2021 final.pdf (2.18 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03374462 , version 1 (12-10-2021)

Identifiants

  • HAL Id : hal-03374462 , version 1

Citer

Sergio da Cunha, Vincent Gerbaud, Nataliya Shcherbakova. EXTREMAL PRINCIPLES IN NON-EQUILIBRIUM THERMODYNAMICS (A NATURE INSPIRATION). European Symposium of Applied Thermodynamics, Jul 2021, Paris, France. ⟨hal-03374462⟩
35 Consultations
33 Téléchargements

Partager

Gmail Facebook X LinkedIn More