Free energy and entropy production rate for a Brownian particle that walks on overdamped medium

Taye, Mesfin Asfaw

doi:10.1103/physreve.94.032111

Cited by 16 publications

(15 citation statements)

References 31 publications

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“…Our previous analysis also suggests [18,19,26] that the entropy extraction rate ḣd can be expressed as…”

Section: A Underdamped Casementioning

confidence: 99%

“…More recently the general expressions for the free energy, entropy production, and entropy extraction rates to a Brownian particle that walks in an overdamped medium was derived [26]. Furthermore, considering a Brownian particle that walks in an underdamped medium, the dependence for entropy production, free energy, and entropy extraction rates on the system parameters was studied [27].…”

Section: Introductionmentioning

confidence: 99%

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Effect of viscous friction on entropy, entropy production and entropy extraction rates in underdamped and overdamped media

Taye

2021

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Considering viscous friction that varies spatially and temporally, the general expressions for entropy production, free energy, and entropy extraction rates are derived to a Brownian particle that walks in an overdamped and underdamped media. Via the well known stochastic approaches to underdamped and overdamped media, the thermodynamic expressions first derived at trajectory level then generalized to an ensemble level. To study the non-equilibrium thermodynamic features of a Brownian particle that hops in a medium where its viscosity varies on time, a Brownian particle that walks on a periodic isothermal medium (in the presence or absence of load) is considered. The exact analytical results depict that in the absence of load f = 0, the entropy production rate ėp approaches the entropy extraction rate ḣd = 0. This is reasonable since any system which is in contact with a uniform temperature should obey the detail balance condition in a long time limit. In the presence of load and when the viscous friction decreases either spatially or temporally, the entropy S(t) monotonously increases with time and saturates to a constant value as t further steps up. The entropy production rate ėp decreases in time and at steady state (in the presence of load), ėp = ḣd > 0. On the contrary, when the viscous friction increases either spatially or temporally, the rate of entropy production as well as the rate of entropy extraction monotonously steps up showing that such systems are inherently irreversible. Furthermore, considering a spatially varying viscosity, the non-equilibrium thermodynamic features of a Brownian particle that hops in a ratchet potential with load is explored. In this case, the direction of the particle velocity is dictated by the magnitude of the external load of f . Far from the stall load, ėp = ḣd > 0 and at stall force ėp = ḣd = 0 revealing the system is reversible at this particular choice of parameter. In the absence of load, ėp = ḣd > 0 as long as a distinct temperature difference is retained between the hot and cold baths. Moreover, considering a multiplicative noise, we explore the thermodynamic features of the model system.

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“…Our previous analysis also suggests [18,19,26] that the entropy extraction rate ḣd can be expressed as…”

Section: A Underdamped Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of viscous friction on entropy, entropy production and entropy extraction rates in underdamped and overdamped media

Taye

2021

Preprint

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“…For a non-Newtonian fluid such blood, it is reasonable to assume that when the temperature of the blood sample increases by 1 degree celsius, its viscosity steps down by 2 percent [16] as γ = B − 2B 100 (T − T R ) where B = 4kg/s is the viscosity of blood at a room temperature (T R = 20 degree celsius) and T is the temperature [17]. The random noise ξ(t) is assumed to be Gaussian white noise satisfying the relations ξ(t) = 0 and ξ…”

Section: The Modelmentioning

confidence: 99%

“…where T is the temperature of the medium. For detailed mathematical analysis, please refer to my previous work [17]. The particle current is then given by…”

Section: The Modelmentioning

confidence: 99%

The physics of Erythrocyte Sedimentation Rate

Taye¹

2019

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An erythrocytes sedimentation rate (ESR) measures how fast a blood sample sediments along a test tube in one hour in a clinical laboratory. Since elevated level of ESR is associated with inflammatory diseases, ESR is one of the routine hematology test in a clinical laboratory. In this paper, the physics of erythrocyte (RBC) sedimentation rate as well as the dynamics of the RBC is explored by modeling the dynamics of the cells as the motion of Brownian particle moving in a viscous medium. The viscous friction of blood γ is considered to decrease as the temperature of the medium increases [1]. The results obtained in this work show that the ESR increases as the number of red blood cells (that bind together in the sedimentation process) steps up. The room temperature also affects the sedimentation rate. As the room temperature rises up, the ESR steps up. Furthermore the dynamics of the RBC along a Westergren pipet that is held in an upright position is explored. The exact analytic result depicts that the velocity of cells increases as the number of cells that form rouleaux steps up. Since our study is performed by considering real physical parameters, the results obtained in this work non only agree with the experimental observations but also helps to understand most hematological experiments that are conducted in vitro.

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“…Some notable works in this regard include, the analytically solvable models depicted in the works [18,19] and the study of thermodynamic features for systems * Electronic address: tayem@wlac.edu that operate in the quantum realm [20][21][22]. Furthermore, for systems that are genuinely driven out of equilibrium, the thermodynamic relations were derived for a Brownian particle that walks in an overdamped medium [23] and underdamped medium [24]. The method of calculating entropy production and extraction rates at ensemble level by first analyzing the thermodynamic relation at trajectory level was introduced in the work [6].…”

Section: Introductionmentioning

confidence: 99%

Exact time-dependent analytical solutions for entropy production rate for a system that operates in a heat bath where its temperature varies linearly in space

Taye

2022

Preprint

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The nonequilibrium thermodynamics feature of a Brownian motor is investigated by obtaining exact time-dependent solutions. This in turn enables us to investigate not only the long time property (steady-state) but also the short time the behavior of the system. The general expressions for the free energy, entropy production ėp(t) as well as entropy extraction ḣd (t) rates are derived for a system that is genuinely driven out of equilibrium by time-independent force as well as by spatially varying thermal background. We show that for a system that operates between hot and cold reservoirs, most of the thermodynamics quantities approach a non-equilibrium steady state in the long time limit. The change in free energy becomes minimal at a steady state. However for a system that operates in a heat bath where its temperature varies linearly in space, the entropy production and extraction rates approach a non-equilibrium steady state while the change in free energy varies linearly in space. This reveals that unlike systems at equilibrium, when systems are driven out of equilibrium, their free energy may not be minimized. The thermodynamic properties of a system that operates between the hot and cold baths are further compared and contrasted with a system that operates in a heat bath where its temperature varies linearly in space along with the reaction coordinate. We show that the entropy, entropy production, and extraction rates are considerably larger for linearly varying temperature case than a system that operates between the hot and cold baths revealing such systems are inherently irreversible. For both cases, in the presence of load or when a distinct temperature difference is retained, the entropy S(t) monotonously increases with time and saturates to a constant value as t further steps up. The entropy production rate ėp decreases in time and at steady state, ėp = ḣd > 0 which agrees with the results shown in the works [18,19]. Moreover, the velocity, as well as the efficiency of the system that operates between the hot and cold baths, are also collated and contrasted with a system that operates in a heat bath where its temperature varies linearly in space along with the reaction coordinate. A system that operates between the hot and cold baths has significantly lower velocity but a higher efficiency in comparison with a linearly varying temperature case.

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Free energy and entropy production rate for a Brownian particle that walks on overdamped medium

Cited by 16 publications

References 31 publications

Effect of viscous friction on entropy, entropy production and entropy extraction rates in underdamped and overdamped media

Effect of viscous friction on entropy, entropy production and entropy extraction rates in underdamped and overdamped media

The physics of Erythrocyte Sedimentation Rate

Exact time-dependent analytical solutions for entropy production rate for a system that operates in a heat bath where its temperature varies linearly in space

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