Fundamentals of nonequilibrium biothermodynamics
Linear nonequilibrium thermodynamics - generalised fluxes and driving forces. Flux conjugation criteria. A steady state close to the equilibrium.
The general linear relation is J = LX (J=the flux, X=the driving force, L=phenomenological coefficient)
When considering any irreversible processes in macroscopic systems, we can distinguish two types of quantities characterizing the process. For example, for the phenomenon of thermal conductivity such quantities are heat flux (Q) and the temperature gradient.
In the case of electrical conductivity, the electrical current I is proportional to the potential gradient (Ohm’s law).
Fick's law is a linear relation between the flow of the diffusing material and the concentration gradient.
The gradients (potential gradient, concentration gradient, temperature gradient) that cause the fluxes are known as DRIVING FORCES and are denoted as X, the fluxes (flows) are usually designated with the symbol J. In the examples given, the laws of these irreversible processes reduce to proportionality between flux and the relevant driving force.
J = L.X (J=flux, X=driving force, L=phenomenological coefficient)
The steady states of many thermodynamic processes can be described by an approach called linear non-equilibrium thermodynamics. In the framework of this approach, the relations between driving forces and fluxes are linear.
Examples:
In non-equilibrium systems with several interacting processes, each flux depends not only on its own driving force but also on the driving forces of the other conjugated processes. This cross-dependence is given by the Onsager equation:
The fluxes Ji are linear functions of the forces Xk. (Lik=phenomenological coefficients).
Flux conjugation: two processes are coupled when their cross coefficient is not zero. Onsager's reciprocal relation states that these cross coefficients are equal (Lik = Lki). In an isotropic medium, only processes of the same tensor character can be coupled (the Curie-Prigogine principle).
Steady state close to equilibrium: according to Prigogine's theorem, a system near equilibrium settles into the steady state with the lowest entropy production its constraints allow.