Work fluctuations in a time-dependent harmonic potential: Rigorous results beyond the overdamped limit

Kwon, Chulan; Noh, Jae Dong; Park, Hyunggyu

doi:10.1103/physreve.88.062102

Cited by 54 publications

(65 citation statements)

References 69 publications

(110 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In Fig. 2, the work distributions are observed to be nearly Gaussian with a small shift of mean from AEjΔFj, agreeing with the theoretical expectation [21]. As a result, P F ðWÞ and P R ð−WÞ almost overlap each other for these rates.…”

Section: Fig 2 (Color Online)supporting

confidence: 75%

“…PðWÞ tends to move to the left towards the origin, as expected from the theoretical study [21]. Figure 3(b) shows the mean values of the work performed in the forward and reverse processes, hWi F and hWi R , as a function of the trap stiffness rate.…”

Section: Fig 2 (Color Online)supporting

confidence: 48%

“…(2) and (3). The analytic expression for the probability distribution of work fluctuation is not known except for special cases: the quasistatic limit ( _ k → 0) and the sudden change limit (j _ kj → ∞) [21]. In the quasistatic process, the particle is in equilibrium at any instant so that hx 2 i ¼ β −1 kðtÞ −1 , as expected from the equipartition theorem.…”

mentioning

confidence: 99%

“…The theoretical approach is more difficult than that for nonequilibrium driven by an external field [9][10][11][12][13][14], and the probability distribution for the work production is not known rigorously. However, there have been recent theoretical works [20,21] where the moments of the work distribution are obtained. On the other hand, no experimental study on nonequilibrium fluctuations for this system has been done to date, partly due to difficulty in modulating the stiffness accurately.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Nonequilibrium Fluctuations for a Single-Particle Analog of Gas in a Soft Wall

2015

Self Cite

View full text Add to dashboard Cite

We investigate the motion of a colloidal particle driven out of equilibrium by a time-varying stiffness of the optical trap that produces persistent nonequilibrium work. Measurements of work production for repeated cycles composed of the compression and expansion processes for the optical potential show huge fluctuations due to thermal motion. Using a precise technique to modulate the stiffness in time, we accurately estimate the probability distributions of work produced for the compression and expansion processes. We confirm the fluctuation theorem from the ratio of the two distributions. We also show that the average values of work for the two processes comply with the Jarzynski equality. This system has an analogy with a gas in a breathing soft wall. We discuss about its applicability to a heat engine and an information engine operated by feedback control. The fluctuation theorem for entropy production in a heat bath was discovered for a deterministic dynamics in the early 1990s [1,2]. Later it was also proved theoretically in a wide class of stochastic systems and extended to other thermodynamic quantities such as work and heat [3][4][5][6][7][8].Since it deals with the stochastic distribution for the fluctuation of a thermodynamic quantity, small systems with large fluctuations have been of interest in experimental studies. The first experiment and the following were done for a colloidal particle driven out of equilibrium by moving the center of the trap [9,10], which is regarded as a prototype of nonequilibrium process driven by an external field. Similar experimental systems were studied, such as a molecule in the atomic force microscopy or a colloidal particle in the optical trap pulled by an external force [11], an electrical dipole driven by a small current [12], and a harmonic oscillator under an external force [13,14]. These systems are well described by the overdamped Langevin equation, and theoretical works were accompanied or performed separately [15,16]. There were also experimental studies for biological systems with unknown dynamical details, such as an RNA molecule unfolded and refolded by optical tweezers [17,18] and a rotating motor protein F 1 -ATPase [19], for which agreement with theory is less accurate.In this Letter, we consider the motion of a colloidal particle in an optical trap with a time-varying stiffness. It is characterized by a different nonequilibrium prototype where a protocol changes the shape of potential in time. The theoretical approach is more difficult than that for nonequilibrium driven by an external field [9][10][11][12][13][14], and the probability distribution for the work production is not known rigorously. However, there have been recent theoretical works [20,21] where the moments of the work distribution are obtained. On the other hand, no experimental study on nonequilibrium fluctuations for this system has been done to date, partly due to difficulty in modulating the stiffness accurately. In this work, we use a liquid crystal device to control the stiffness p...

show abstract

Section: Fig 2 (Color Online)supporting

confidence: 75%

Section: Fig 2 (Color Online)supporting

confidence: 48%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Nonequilibrium Fluctuations for a Single-Particle Analog of Gas in a Soft Wall

2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…In contrast to the previous works, our study focuses on the role of the slow and fast variable. Harmonic systems are analytically tractable [26][27][28][29][30][31]. We derive the formula for the entropy productions by the slow and fast variables as a function of the coupling constant, which will shed a light on the effect of the coarse graining.…”

Section: Introductionmentioning

confidence: 99%

Hidden entropy production by fast variables

Chun

Noh

2015

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

We investigate nonequilibrium underdamped Langevin dynamics of Brownian particles that interact through a harmonic potential with coupling constant K and are in thermal contact with two heat baths at different temperatures. The system is characterized by a net heat flow and an entropy production in the steady state. We compare the entropy production of the harmonic system with that of Brownian particles linked with a rigid rod. The harmonic system may be expected to reduce to the rigid rod system in the infinite K limit. However, we find that the harmonic system in the K → ∞ limit produces more entropy than the rigid rod system. The harmonic system has the center of mass coordinate as a slow variable and the relative coordinate as a fast variable. By identifying the contributions of the degrees of freedom to the total entropy production, we show that the hidden entropy production by the fast variable is responsible for the extra entropy production. We discuss the K dependence of each contribution.

show abstract

Thermodynamic work statistics for Ornstein–Uhlenbeck-type heat baths

Jiménez–Aquino

Sánchez-Salas

2018

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

Work fluctuations in a time-dependent harmonic potential: Rigorous results beyond the overdamped limit

Cited by 54 publications

References 69 publications

Nonequilibrium Fluctuations for a Single-Particle Analog of Gas in a Soft Wall

Nonequilibrium Fluctuations for a Single-Particle Analog of Gas in a Soft Wall

Hidden entropy production by fast variables

Thermodynamic work statistics for Ornstein–Uhlenbeck-type heat baths

Contact Info

Product

Resources

About