Nonlinear reciprocity and the maximum entropy formalism

• Published in: Physica A 1989-07, Vol.158 (2), p.672-690
• Main Authors: Nettleton, R.E., Freidkin, E.S.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Physics
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/0378-4371(89)90385-3

The maximum entropy formalism calculates a phase-space distribution, p(x) , which maximizes the information-theoretic entropy subject to specified values of internal energy and state variables α i and η i ( i = 1, …, n). The latter are averages, calculated from p , of dynamical functions A i and A i ≡ iLA i , respectively, where L is the Liouville operator. From p , one extracts a fluctuation distribution g(a, v) for the values of the A and A ̊ . A kinetic equation for the fluctuation distribution has been derived by Grabert using projection operators appropriate to a system in thermal contact with its surroundings, and g is proposed as an ansatz for its solution. From the first moments of the kinetic equation, after introduction therein of g , one extracts phenomenological equations for ⋗a i and ⋗h i whose terms can be grouped to exhibit Onsager symmetry, even when nonlinear terms are included. The groupings can be affected exactly, but not uniquely.