Stochastic thermodynamics with odd controlling parameters

Li, Geng; Tu, Z. C.

doi:10.1103/physreve.100.012127

Cited by 14 publications

(5 citation statements)

References 61 publications

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“…they are positionlike physical quantities. One extension to our work is to consider variables that have odd parity under time reversal such as velocity [58][59][60].…”

Section: Discussionmentioning

confidence: 99%

Unified formalism for entropy production and fluctuation relations

Yang

Qian

2020

Phys. Rev. E

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Stochastic entropy production, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the change in the statistical properties of observables due to reversals can be represented by a change in the probability measure. We consider operators on the space of probability measure that induce changes in the statistical properties of a process, and formulate entropy productions in terms of these change-of-probability-measure (CPM) operators. This mathematical underpinning of the origin of entropy productions allows us to achieve an organization of various forms of fluctuation relations: All entropy productions have a non-negative mean value, admit the integral fluctuation theorem, and satisfy a rather general fluctuation relation. Other results such as the transient fluctuation theorem and detailed fluctuation theorems then are derived from the general fluctuation relation with more constraints on the operator of a entropy production. We use a discrete-time, discrete-state-space Markov process to draw the contradistinction among three reversals of a process: time reversal, protocol reversal and the dual process. The properties of their corresponding CPM operators are examined, and the domains of validity of various fluctuation relations for entropy productions in physics and chemistry are revealed. We also show that our CPM operator formalism can help us rather easily extend other fluctuations relations for excess work and heat, discuss the martingale properties of entropy productions, and derive the stochastic integral formulas for entropy productions in constant-noise diffusion process with Girsanov theorem. Our formalism provides a general and concise way to study the properties of entropy-related quantities in stochastic thermodynamics and information theory. *

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“…they are positionlike physical quantities. One extension to our work is to consider variables that have odd parity under time reversal such as velocity [58][59][60].…”

Section: Discussionmentioning

confidence: 99%

Unified formalism for entropy production and fluctuation relations

Yang

Qian

2020

Phys. Rev. E

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“…In the limit λ/J 1, however, we expect that the features of the classical Heisenberg spin chain will take over for the spin transport at long times destroying the KPZ superdiffusion. In this limit we expect diffusive behaviour with possible logarithmic corrections [27,[37][38][39][40][41][42][43][44][45][46][47][48]. For integrability-breaking perturbations which do not respect spin-symmetry, the KPZ superdiffusion is immediately lost [25].…”

Section: (B)mentioning

confidence: 99%

Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability

Roy¹,

Dhar²,

Spohn³

et al. 2022

Preprint

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“…For stochastic systems, it is possible to achieve a finite-rate transition between two designated equilibrium states [27,28] via a non-equilibrium path, and also to reduce the dissipated work [29]. Another recent advance is the shortcut-to-isothermality (ScI) transition [30,31] in which instantaneous equilibrium (ieq) at a fixed temperature is maintained at all moments during the finite speed transition, which was demonstrated experimentally in a Brownian particle under a moving harmonic potential [32] and trapping potentials of varying stiffness [33,34]. The ScI transition manifests the idea of instantaneous equilibrium which generalizes the notion of equilibrium, and a work relation for the symmetry of the ScI of forward and reverse processes was established [13].…”

Section: Introductionmentioning

confidence: 99%

Instantaneous equilibrium Transport for Brownian systems under time-dependent temperature and potential variations: Reversibility, Heat and work relations, and Fast Isentropic process

Jun,

Lai

2021

Preprint

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The theory of constructing instantaneous equilibrium (ieq) transition under arbitrary timedependent temperature and potential variation for a Brownian particle is developed. It is shown that it is essential to consider the underdamped dynamics for temperature-changing transitions.The ieq is maintained by a time-dependent auxiliary position and momentum potential, which can be calculated for given time-dependent transition protocols. Explicit analytic results are derived for the work and heat statistics, energy, and entropy changes for harmonic and non-harmonic trapping potential with arbitrary time-dependent potential parameters and temperature protocols. Numerical solutions of the corresponding Langevin dynamics are computed to confirm the theoretical results. Although ieq transition of the reverse process is not the time-reversal of the ieq transition of the forward process due to the odd-parity of controlling parameters, their phase-space distribution functions restore the time-reversal symmetry, and hence the energy and entropy changes of the ieq of the reverse process are simply the negative of that of the forward process. Furthermore, it is shown that it is possible to construct an ieq transition that has zero entropy production at a finite transition rate, i.e., a fast ieq isentropic process, and is further demonstrated by explicit Langevin dynamics simulations. Our theory provides fundamental building blocks for designing controlled microscopic heat engine cycles. Implications for constructing an efficient Brownian heat engine are also discussed.

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Stochastic thermodynamics with odd controlling parameters

Cited by 14 publications

References 61 publications

Unified formalism for entropy production and fluctuation relations

Unified formalism for entropy production and fluctuation relations

Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability

Instantaneous equilibrium Transport for Brownian systems under time-dependent temperature and potential variations: Reversibility, Heat and work relations, and Fast Isentropic process

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