Reciprocity Relations for Nonlinear Systems

Reciprocity relations for open nonlinear systems in variable fields

“…Kinetic coefficients (30) and (31) for the response to mechanical and thermodynamic inputs were determined sensu Kubo [2] formally (without specifying the physical mechanism of this response). The derivation of these relations and reciprocity relation (34) based on them is valid in the Markovian relaxation approximation if the unperturbed Hamiltonian is stationary and the unperturbed system is in a quasi-equilibrium state (11). In addition, the system remains stable under the influence of a perturbation that may be presented as a sum of products of a classical specified force by an operator corresponding to an external dynamic variable and an operator of Markovian relaxation to the quasi-equilibrium state.…”

“…Here, is the Massieu−Planck functional for a quasi-equilibrium system in external fields [17], θ(t, r) = 1/(kT (t, r)), k is the Boltzmann constant, T (t, r) is the local temperature, and µ i (t, r) is the local chemical potential of particles of the ith component. An inhomogeneous and nonstationary distribution of functions and operators in (11) and (12) may be established if the system comes into contact with several different thermostats and reservoirs.…”

“…At this stage, we consider the components of magnetic induction on which quasiequilibrium distribution (11) does depend explicitly as separate forces that are not included into vector F of mechanical forces. Quasi-equilibrium distribution (11) then does not depend explicitly on mechanical forces. Since ŝ * iα (t, r) = − ŝiα (t, r), we obtain the following from the first Eq.…”

“…(13 , T(t,r), B(t,r)) = ρ * km (−F(t,r), T(t,r), −B(t,r)). Thus, magnetic field B on which quasi-equilibrium distribution (11) does depend explicitly may be regarded as a mechanical force and included into vector F. With the Hermitian nature of the operator taken into account, we then obtain ρkm (F(t, r), T(t, r)) = ρmk (−F(t, r)T(t, r)). (20) Equation ( 17) is equivalent to integral equation…”

“…Notably, significant violations of the reciprocity relations between spin-dependent Peltier and Seebeck effects, which are attributable to the nonlinearity of the voltage-current relationship at strong transport currents, were observed [10]. The reciprocity relations for nonlinear systems are satisfied only in particular cases (e.g., for closed systems in a constant and homogeneous magnetic field [11]). It was demonstrated experimentally that these relations are satisfied within the measurement accuracy [12].…”