Abstract
Biological systems are far from thermodynamic equilibrium. Concentration gradients and electrostatic potential differences are the driving forces for diffusive currents and chemical reactions. In this chapter, we present the basic ingredients of nonequilibrium thermodynamics. We derive continuity equations for mass and energy. Entropy production is a bilinear function of the thermodynamic forces which vanish at equilibrium. Close to equilibrium, the fluxes can be approximated as linear functions of the forces and the entropy production as a positive definite symmetric quadratic form. Finally, we discuss stationary states which are characterized by a minimum of entropy production, which is compatible with certain external conditions.
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Notes
- 1.
A more general discussion can be found in [37].
- 2.
The definition of the heat flux is not unique in the case of simultaneous diffusion and heat transport. Our definition is in analogy to the relation \(T\mathrm{d}S=\mathrm{d}H-V\mathrm{d}p-\sum _{k}\mu _{k}\mathrm{d}N_{k}\) for an isobaric system. With this convention the diffusion flux does not depend on the temperature gradient explicitly.
- 3.
only a set of independent fluxes should be used here.
- 4.
Fluxes with different tensorial character are not coupled.
- 5.
Especially the Onsager coefficients have to be constants.
- 6.
This is connected to the Seebeck effect.
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Problems
Problems
10.1
Entropy Production by Chemical Reactions
Consider an isolated homogeneous system with \(T=\text {const}\) and \(\mu _{k}=\text {const}\) but nonzero chemical affinities
and determine the rate of entropy increase.
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Scherer, P.O.J., Fischer, S.F. (2017). Non-equilibrium Thermodynamics. In: Theoretical Molecular Biophysics. Biological and Medical Physics, Biomedical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55671-9_10
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DOI: https://doi.org/10.1007/978-3-662-55671-9_10
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