Eur. Phys. J. B (2015) 88: 146
https://doi.org/10.1140/epjb/e2015-60179-1

Regular Article

Work distribution function for a Brownian particle driven by a nonconservative force

¹ Department of Physics, Indian Institute of Technology, 208 016 Kanpur, India
² Department of Protein Chemistry and Technology, Central Food Technological Research Institute, 570 020 Mysore, India

^a e-mail: sutapam@iitk.ac.in
^b On leave from Department of Physics, Indian Institute of Technology, 208 016 Kanpur, India.

Received: 6 March 2015
Received in final form: 5 May 2015
Published online: 3 June 2015

Abstract

We derive the distribution function of work performed by a harmonic force acting on a uniformly dragged Brownian particle subjected to a rotational torque. Following the Onsager and Machlup’s functional integral approach, we obtain the transition probability of finding the Brownian particle at a particular position at time t given that it started the journey from a specific location at an earlier time. The difference between the forward and the time-reversed form of the generalized Onsager-Machlup’s Lagrangian is identified as the rate of medium entropy production which further helps us develop the stochastic thermodynamics formalism for our model. The probability distribution for the work done by the harmonic trap is evaluated for an equilibrium initial condition. Although this distribution has a Gaussian form, it is found that the distribution does not satisfy the conventional work fluctuation theorem.