Abstract
An extended fluctuation theorem is the new type of fluctuation theorem for heat, proposed by van Zon and Cohen. In this chapter, we study it from the view point of rare trajectory of particle. We especially consider a Brownian particle on a moving periodic potential, and take a large limit of the period and the height of the potential, which describes the situation where the particle is trapped in a single potential. During this limit, we focus on the large deviation function of the heat dissipation of the particle that is the key ingredient of the extended fluctuation theorem, and also we focus on a biased ensemble that gives the statistics of rare-trajectory. From the boundary layer analysis, we construct these functions, and show that the singularity appears with the remarkable behaviour of the particle to climb up the potential, characterised by a negative temperature.
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Notes
- 1.
In this calculation, we use the condition (4.7).
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Nemoto, T. (2016). van Zon–Cohen Singularity and a Negative Inverse Temperature. In: Phenomenological Structure for the Large Deviation Principle in Time-Series Statistics. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-287-811-3_4
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DOI: https://doi.org/10.1007/978-981-287-811-3_4
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