Eur. Phys. J. B (2014) 87: 195
https://doi.org/10.1140/epjb/e2014-50379-6

Regular Article

Fluctuation theorems for excess and housekeeping heat for underdamped Langevin systems

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

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

Received: 10 June 2014
Received in final form: 8 July 2014
Published online: 3 September 2014

Abstract

We present a simple derivation of the integral fluctuation theorems for excess and housekeeping heat for an underdamped Langevin system, without using the concept of dual dynamics. In conformity with the earlier results, we find that the integral fluctuation theorem for housekeeping heat holds when the steady state distributions are symmetric in velocity, whereas there is no such requirement for the excess heat. We first prove the integral fluctuation theorem for the excess heat, and then show that it naturally leads to the integral fluctuation theorem for housekeeping heat. We also derive the modified detailed fluctuation theorems for the excess and housekeeping heats.