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We propose an application of fiber bundles to counting statistics. Theframework of the fiber bundles gives a splitting of a cumulant generatingfunction for current in a stochastic process, i.e., contributions from thedynamical phase and the geometric phase. We will show that the introducednoncyclic geometric phase is related to a kind of excess contributions, whichhave been investigated a lot in nonequilibrium physics. Using a specificnonequilibrium model, the characteristics of the noncyclic geometric phase arediscussed; especially, we reveal differences between a geometric contributionfor the entropy production and the `excess entropy production' which has beenused to discuss the second law of steady state thermodynamics.

Noncyclic geometric phase in counting statistics and its role as an excess contribution