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On the derivation of the Onsager relations from the Master equation

✍ Scribed by M. Moreau

Publisher
Springer
Year
1975
Tongue
English
Weight
337 KB
Volume
1
Category
Article
ISSN
0377-9017

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✦ Synopsis

The asymptotical properties of a Markov system with discrete states are derived from the Master equation by using the quadratic approximate form of entropy.

In particular, symmetry relations equivalent to the Onsager reciprocal relations are established for time reversal invariant systems.

i.

The Onsager relations may be derived from the hypotheses of the detailed balance, or more generally from time reversal invariance, either by using the Einstein theory of fluctuations [I], or alternatively the Boltzmann equation [2,3]. In fact, it will be shown in this paper that similar relations follow directly from the Master equation for a time reversal invariant Markov system.

Taking the case of a Markov system with a finite number of states, we discuss the symmetry properties of the transition probabilities at first. Then, using the quadratic approximate form of entropy, we study the tendency towards equilibrium, and we derive the Onsager relations by expressing the time-varying probabilities in terms of the average values of convenient constant physical quantities.

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