Koichiro Matsuno

Probabilistic kinetics of macroprocesses in broken microscopic reversibility

Probabilistic kinetics following the Pauli master equation without microscopic reversibility determines an asymptotic structure of macroprocesses in a coarse-grained phase space of many degrees of freedom. The structure, which is asymptotically realized, minimizes its irreversible decay rate among various candidates. This least irreversible decay rate is consistent with the assertion for the minimum K-entropy which has been argued to apply to the nonequilibrium asymptotic state. The irreversible decay rate is a state function characteristic of macrostructure on a coarse-grained time scale. Macrofluctuations, which always appear around the asymptote as fluctuations of the state function, do not obey the central limit theorem, implying that fluctuations whose characteristic times are not less than some finite value are never excluded.

LOW FREQUENCY CURRENT FLUCTUATIONS IN A GaAs GUNN DIODE

Low frequency noise spectrum and electrical conductivity of a GaAs Gunn diode are presented. Based on these results, we suggest that the observed FM noise spectrum of Gunn oscillators with −9 dB/octave slope of noise‐to‐carrier ratio may also be due to current fluctuations with l/f characteristic resulting from electron trapping.

Ergodicity of observable and ergodic hypothesis in Markovian kinetics

The time average of any observable, which evolves following an irreducible Markov process with countable states each of which is a persistent state, equals the ensemble average of the same quantity if and only if the corresponding master equation does not exhibit the accumulation of its eigenvalues around the infinitesimal neighborhood of the point with the value zero and if the steady distribution as the eigenfunction with the eigenvalue zero is uniform. The nonuniform steady distribution invalidates the ergodicity of observable. The principle of a priori equal weight is identical to the ergodicity of observable.

Ergodicity of quantum mechanical systems

The ergodicity of pure quantum states is maintained in the space of orthonormal quantum states which diagonalizes an observable. The ergodicity of mixed quantum states, which is met in quantum statistical mechanics admitting an ensemble of many similar systems, is identical to the principle of equal a priori probabilities.

Asymptotic behavior of Markoffian kinetics

The ergodic state with the least mean recurrence time in an irreducible Markoffian process having countable states, between any pair of which transition probability rates are definable, is the state with the least irreversible decay rate if neither the microscopic reversibility nor the doubly stochastic property holds.

Ergodic state with least mean recurrence time in Markovian kinetics

We present a proof of the theorem that the ergodic state with the least mean recurrence time in an irreducible Markov process having countable states is identical, with probability unity, to the state with the least irreversible decay rate if neither microscopic reversibility nor the doubly stochastic property holds.