Thermodynamic length, time, speed, and optimum path to minimize entropy production

Diósi, L.; Kulacsy, K.; Lukács, B.; Rácz, A.
December 1996
Journal of Chemical Physics;12/22/1996, Vol. 105 Issue 24, p11220
Academic Journal
In addition to the Riemannian metricization of the thermodynamic state space, local relaxation times offer a natural time scale, too. Generalizing existing proposals, we relate a thermodynamic time scale to the standard kinetic coefficients of irreversible thermodynamics. The notion of thermodynamic speed is generalized to higher dimensions. Criteria for minimum entropy production in slow, slightly irreversible processes are discussed. Euler-Lagrange equations are derived for optimum thermodynamic control for fixed clock time period as well as for fixed thermodynamic time period. It is emphasized that the correct derivation of the principle of constant thermodynamic speed, proposed earlier by others, requires the entropy minimization at fixed thermodynamic time instead of clock-time. Most remarkably, optimum paths are Riemannian geodesics which would not be the case had we used ordinary time. To interpret thermodynamic time, an easy-to-implement stepwise algorithm is constructed to realize control at constant thermodynamic speed. Thermodynamic time is shown to correspond to the number of steps, and the sophisticated task of determining thermodynamic time in real control problems is achieved by measuring ordinary intensive variables.


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