We derive general expressions for the free energy, entropy production, and entropy extraction rates for a Brownian particle that walks in a viscous medium where the dynamics of its motion is governed by the Langevin equation. It is shown that, when the system is out of equilibrium, it constantly produces entropy and at the same time extracts entropy out of the system. Its entropy production and extraction rates decrease in time and saturate to a constant value. In the long-time limit, the rate of entropy production balances the rate of entropy extraction and, at equilibrium, both entropy production and extraction rates become zero. Moreover, considering different model systems, not only do we investigate how various thermodynamic quantities behave in time but also we discuss the fluctuation theorem in detail.

No abstract

No abstract

The expressions for entropy production, free energy, and entropy extraction rates are derived for a Brownian particle that walks in an underdamped medium. Our analysis indicates that as long as the system is driven out of equilibrium, it constantly produces entropy at the same time it extracts entropy out of the system. At steady state, the rate of entropy productionėp balances the rate of entropy extractionḣ d. At equilibrium both entropy production and extraction rates become zero. The entropy production and entropy extraction rates are also sensitive to time. As time progresses, both entropy production and extraction rates increase in time and saturate to constant values. Moreover employing microscopic stochastic approach, several thermodynamic relations for different model systems are explored analytically and via numerical simulations by considering a Brownian particle that moves in overdamped medium. Our analysis indicates that the results obtained for underdamped cases quantitatively agree with overdamped cases at steady state. The fluctuation theorem is also discussed in detailed.

We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. It is shown that the efficiency of such Brownian heat engine is far from Carnot efficiency even at quaistatic limit. At quasistatic limit, the efficiency of the heat engine approaches the efficiency of endoreversible engine η = 1 − Tc/T h [23]. On the other hand, the maximum power efficiency of the engine approaches. Moreover, the dependence of the current as well as the efficiency on the model parameters is explored analytically by omitting the heat exchange via the kinetic energy. In this case we show that the optimized efficiency always lies between the efficiently at quaistatic limit and the efficiency at maximum power. On the other hand, the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If one includes the heat exchange at the boundary of the heat baths, the efficiency of the engine becomes much smaller than the Carnot efficiency. In addition, the dependence for the coefficient of performance of the refrigerator on the model parameters is explored by including the heat exchange via the potential and kinetic energy. We show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t as well as the external load dictate the direction of the particle velocity. Moreover the performance of the heat engine improves with time. At large t (steady state),the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value.