Thermodynamic uncertainty relation for Langevin dynamics by scaling time

Fu, Rueih-Sheng; Gingrich, Todd R.

doi:10.1103/physreve.106.024128

Cited by 7 publications

(8 citation statements)

References 44 publications

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“…Dissipation is defined as the heat released from the system to the medium via the friction and thermal noise and thus is expressed as ( 31 , 42 , 57 ):

…”

Section: Resultsmentioning

confidence: 99%

“…4 A . The trade-off between dissipation and current precision can be described by the TUR recently discovered in far-from-equilibrium statistical mechanics ( 34 – 42 ). For Markovian systems such as systems driven by overdamped Langevin dynamics, the TUR states that the current precision is lower-bounded by the inverse of entropy production Σ = 𝒬/ T as refs.…”

Section: Resultsmentioning

confidence: 99%

“…Hence, a smaller bound is derived as ref. 40 – 42

Υ is the so-called dynamical activity , defined as

…”

Section: Resultsmentioning

confidence: 99%

“…As the field gets stronger, the dissipation increases while the relative fluctuation of currents decreases. To characterize this trade-off relation, we apply the thermodynamic uncertainty relation ( 34 – 42 ).…”

mentioning

confidence: 99%

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Colloidal superionic conductors

Lin

Cruz

2023

Proc. Natl. Acad. Sci. U.S.A.

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Nanoparticles with highly asymmetric sizes and charges that self-assemble into crystals via electrostatics may exhibit behaviors reminiscent of those of metals or superionic materials. Here, we use coarse-grained molecular simulations with underdamped Langevin dynamics to explore how a binary charged colloidal crystal reacts to an external electric field. As the field strength increases, we find transitions from insulator (ionic state), to superionic (conductive state), to laning, to complete melting (liquid state). In the superionic state, the resistivity decreases with increasing temperature, which is contrary to metals, yet the increment decreases as the electric field becomes stronger. Additionally, we verify that the dissipation of the system and the fluctuation of charge currents obey recently developed thermodynamic uncertainty relation. Our results describe charge transport mechanisms in colloidal superionic conductors.

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“…Dissipation is defined as the heat released from the system to the medium via the friction and thermal noise and thus is expressed as ( 31 , 42 , 57 ):

…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…Hence, a smaller bound is derived as ref. 40 – 42

Υ is the so-called dynamical activity , defined as

…”

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Colloidal superionic conductors

Lin

Cruz

2023

Proc. Natl. Acad. Sci. U.S.A.

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“…In recent years, there has been growing interest in understanding the precision of observables in quantum thermodynamic regimes [8][9][10][11][12][13][14][15][16][17][18]. Especially, when in the equilibrium Boltzmann state, the system density operator is then proportional to exp(−β Ĥ) with β ≡ 1/(k B T ) being the inverse temperature and Ĥ the Hamiltonian.…”

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confidence: 99%

On the lower bound of the Heisenberg uncertainty product in the Boltzmann states

Wang

2023

EPL

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The uncertainty principle lies at the heart of quantum mechanics, as it describes the fundamental trade-off between the precision of position and momentum measurements. In this work, we study the quantum particle in the Boltzmann states and derive a refined lower bound on the product of ∆x and ∆p. Our new bound is expressed in terms of the ratio between ∆x and the thermal de Broglie wavelength, and provides a valuable tool for characterizing thermodynamic precision. We apply our results to the Brownian oscillator system, where we compare our new bound with the well-known Heisenberg uncertainty principle. Our analysis shows that our new bound offers a more precise measure of the thermodynamic limits of precision.

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Variance sum rule: proofs and solvable models

Di Terlizzi,

Baiesi,

Ritort

2024

New J. Phys.

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We derive, in more general conditions, a recently introduced variance sum rule (VSR) [I. Di Terlizzi et al., 2024 Science 383, 971] involving variances of displacement and force impulse for overdamped Langevin systems in a nonequilibrium steady state (NESS). This formula allows visualising the effect of nonequilibrium as a deviation of the sum of variances from normal diffusion 2Dt, with D the diffusion constant and t the time. From the VSR, we also derive formulas for the entropy production rate σ that, differently from previous results, involve second-order time derivatives of position correlation functions. This novel feature gives a criterion for discriminating strong nonequilibrium regimes without measuring forces. We then apply and discuss our results to three analytically solved models: a stochastic switching trap, a Brownian vortex, and a Brownian gyrator. Finally, we compare the advantages and limitations of known and novel formulas for σ in an overdamped NESS.

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Thermodynamic uncertainty relation for Langevin dynamics by scaling time

Cited by 7 publications

References 44 publications

Colloidal superionic conductors

Colloidal superionic conductors

On the lower bound of the Heisenberg uncertainty product in the Boltzmann states

Variance sum rule: proofs and solvable models

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