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We develop a new interpretation of the geometric phase in evolution with anon-Hermitian real value Hamiltonian by relating it to the angle developedduring the parallel transport along a closed curve by a unit vector triad inthe 3D-Minkovsky space. We also show that this geometric phase is responsiblefor the anholonomy effects in stochastic processes considered in [N. A.Sinitsyn and I. Nemenman, EPL {\bf 77}, 58001 (2007)], and use it to derive thestochastic system response to periodic parameter variations.

Geometric phase for non-Hermitian Hamiltonian evolution as anholonomy of a parallel transport along a curve