Converting Non Homogeneous System To Homogeneous System And Determination Of Thermodynamic Quantities

Motion of a Brownian particle in a high friction nonhomogeneous medium in a ratchetrnpotential with spatially varying temperature is considered. Employing the appropri-rnate transformation for Langevin equation describing its motion, the expression forrnthe equivalent load in corresponding homogeneous medium is formulated. The steadyrnstate particle current expressions for both cases are calculated as a function of cor-rnresponding model parameters. The behavior of equivalent load with 'noise intensity'rnand currents with their corresponding model parameters are explored and analyzed.rnWe show that the increase in noise intensity to large value makes the load to saturaternto a limiting value. We also consider Brownian particle in a high friction with bothrnconstant and space dependent temperature background. The system is taken awayrnfrom equilibrium by either varying the barrier height in space dependent temperaturernor by varying load in constant temperature system with time. Using Sekimoto's [22]rnenergetic framework we calculated the expression for change in Helmholtz free energyrnin the two models that we considered

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