Abstract
The Onsager symmetry relations are applied to the study of electrokinetic effects and of thermomechanical effects. In the latter case the relation between thermomolecular pressure difference and the heat of transfer is calculated, for comparison, also for Knudsen gases in a classical kinetic model. The characterization of stationary states as states of minimum entropy production are studied. The determination of stationary states, their stability and the principles of Le Chatelier and of Le Chatelier–Braun, find their correct explanation within the context of the thermodynamical theory of stationary states. The model by Prigogine and Waime is presented as an example. Within the theory of fluctuations in an isolated thermodynamical system, the decay of fluctuations are treated with the formalism of linear irreversible processes and the symmetry properties of the linear phenomenological matrix is derived from the postulate of time reversal symmetry for microscopic physics.
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- 1.
The “degrees of freedom” are the terms that make up the expression total energy of the system. In the case of polyatomic molecules we should add more degrees of freedom that give account of the rotational and vibrational motions.
- 2.
Energy can be transferred between the two vessels even if the flow of matter is zero.
- 3.
For isolated systems the property is obviously verified: at equilibrium (stationary state), the entropy production is zero (minimum).
- 4.
See Sect. 4.3.1.
- 5.
Chemical reactions are excluded and, more in general, let’s treat the n extensive quantities \(E_{\rho }\) as a kind of “conserved quantities”. If not, the expression for the entropy production would contain additional terms not coupled with the terms that describe the exchanges between the two phases. The changes due to interactions with the outside world are due to interactions with “third systems”.
- 6.
For the fluxes we choose as positive the direction \(\mathrm {I}\rightarrow \mathrm {II}\).
- 7.
We see that, in the stationary case, the flows represent the transfer, between the two external constraining systems, of a specific physical quantity the meaning of which depends, of course, on the choice of the state variables \({\mathcal {E}}_{\rho }^{\,\mathrm {I, II}}\).
- 8.
This statement will be proved in Sect. 15.2.3.
- 9.
The reader should avoid the mistake of attributing the classification “accurate” and “less accurate” any hierarchy of merit. It is not true that to be more accurate (in this scientific context) is “better” than being less accurate. These are two different perspectives that, of course, must be integrated but which lead to different representations. By analogy, we can observe the details of the single stones (fossils and minerals) but if we did not consider the shape, altitude and the distribution of the mountain ranges, we would not have conceived the theory of continental collision and then of plate tectonics.
- 10.
Indeed the presence of fluctuations can be conceived equally well in a continuum.
- 11.
We are dealing with deviations of the state around a state of equilibrium in an isolated system. In this case the entropy is maximum in the equilibrium configuration.
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Saggion, A., Faraldo, R., Pierno, M. (2019). Irreversible Processes: Applications. In: Thermodynamics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-26976-0_15
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DOI: https://doi.org/10.1007/978-3-030-26976-0_15
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