Eur. Phys. J. B (2014) 87: 141
https://doi.org/10.1140/epjb/e2014-50219-9

Regular Article

Exchange fluctuation theorems for a chain of interacting particles in presence of two heat baths

¹ Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, 130-722 Seoul, Republic of Korea
² Institute of Physics, Sachivalaya Marg, 751005 Bhubaneswar, India

^a e-mail: lahiri@kias.re.kr

Received: 31 March 2014
Received in final form: 8 May 2014
Published online: 23 June 2014

Abstract

The exchange fluctuation theorem for heat exchanged between two systems at different temperatures, when kept in direct contact, has been investigated by Jarzynski and Wójcik [Phys. Rev. Lett. 92, 230602 (2004)]. We extend this result to the case where two Langevin reservoirs at different temperatures are connected via a conductor made of interacting particles, and are subjected to an external drive or work source. The Langevin reservoirs are characterized by Gaussian white noise fluctuations and concomitant friction coefficients. We first derive the Crooks theorem for the ratio between forward and reverse paths, and discuss the first law in this model. Then we derive the modified detailed fluctuation theorems (MDFT) for the heat exchanged at each end. These theorems differ from the usual form of the detailed fluctuation theorems (DFT) in literature, due the presence of an extra multiplicative factor. This factor quantifies the deviation of our MFDT from the DFT. Finally, we numerically study our model, with only two interacting particles for simplicity.