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

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.     

Dilute Solution Properties of Styrene-N-Butyl Methacrylate (65:35) Copolymer: Short- and Long-Range Interaction of the Polymer Chain

Abstract

Viscosity and light-scattering data on styrene-n-butyl methacrylate (65:35) in chloroform are presented and tested by the two-parameter theoretical relations. The short-range interactions K and A and the long-range interaction parameter B have been calculated by different equations, using intrinsic viscosity and second virial coefficient data. These are then compared to the values of the homopolymer polystyrene. The conformation or the steric factor for the polymer chain has also been calculated. The excluded volume parameter Z, which is related to both the short- and long-range parameters, has been evaluated along with the expansion factor α _n . The higher value of the short-range parameters and the conformation factor compared to the parent styrene homopolymer is attributed to the effect of unlike monomer interactions causing extension of the polymer chain. An increase in the restriction of the internal rotation of side chains about the C-C bonds is also suggested. The excess interaction parameter has a negative value. The expansion factor α _n has been related to the excluded volume factor Z and the coefficient C is in close agreement with the theoretically calculated value of Yamakawa and Tanaka.