General Criterion for Harmonicity

Proesmans, Karel; Vandebroek, Hans; Broeck, C. Van den

doi:10.1103/physrevlett.119.147803

Cited by 4 publications

(4 citation statements)

References 20 publications

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“…The first surprise arises with d = 4: the LDF is purely quadratic up to full extension |x| = 1. This result was anticipated in [27] from a general criterion for such "perfect harmonicity". Turning to d = 5, we note that the LDF is still convex, but with inflection points at |x| = 1.…”

Section: The Large Deviation Functionmentioning

confidence: 62%

Phase transitions in persistent and run-and-tumble walks

Proesmans

Toral

Broeck

2020

Physica A: Statistical Mechanics and its Applications

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We calculate the large deviation function of the end-to-end distance and the corresponding extension-versusforce relation for (isotropic) random walks, on and off-lattice, with and without persistence, and in any spatial dimension. For off-lattice random walks with persistence, the large deviation function undergoes a first order phase transition in dimension d > 5. In the corresponding force-versus-extension relation, the extension becomes independent of the force beyond a critical value. The transition is anticipated in dimensions d = 4 and d = 5, where full extension is reached at a finite value of the applied stretching force. Full analytic details are revealed in the run-and-tumble limit. Finally, on-lattice random walks with persistence display a softening phase in dimension d = 3 and above, preceding the usual stiffening appearing beyond a critical value of the force.

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Section: The Large Deviation Functionmentioning

confidence: 62%

Phase transitions in persistent and run-and-tumble walks

Proesmans

Toral

Broeck

2020

Physica A: Statistical Mechanics and its Applications

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“…First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension is non-Gaussian, our model would correspond to non-harmonic interactions between neighboring monomers [53].…”

Section: J Stat Mech (2021) 103208mentioning

confidence: 98%

First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension

Mori¹,

Gradenigo²,

Majumdar³

2021

J. Stat. Mech.

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We consider a single run-and-tumble particle (RTP) moving in one dimension. We assume that the velocity of the particle is drawn independently at each tumbling from a zero-mean Gaussian distribution and that the run times are exponentially distributed. We investigate the probability distribution P (X, N ) of the position X of the particle after N runs, with N 1. We show that in the regime X ∼ N 3/4 the distribution P (X, N ) has a large deviation form with a rate function characterized by a discontinuous derivative at the critical value X = X c > 0. The same is true for X = −X c due to the symmetry of P (X, N ). We show that this singularity corresponds to a first-order condensation transition: for X > X c a single large jump dominates the RTP trajectory. We consider the participation ratio of the single-run displacements as the order parameter of the system, showing that this quantity is discontinuous at X = X c . Our results are supported by numerical simulations performed with a constrained Markov chain Monte Carlo algorithm.

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“…The non self-averaging nature of fluctuations in stochastic efficiency and other quantities requires detailed understanding of full probability distributions as opposed to the average behavior [41,42]. Large deviation properties of such distributions are recently under theoretical investigations [45,46,47,48,49,50,51]. Research on fluctuation relations for heat engines [52,53,54] are being pursued.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Brownian refrigerator

Rana

Pal

Saha

et al. 2016

Physica A: Statistical Mechanics and its Applications

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We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the system cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown analytically that in the quasistatic regime the system can also act as stochastic heater, depending on the bath temperatures. Interestingly, in non-quasistatic regime, our system can even work as a stochastic heat engine for certain range of cycle time and bath temperatures. We show that the operation of this engine is not reliable. The fluctuations of stochastic efficiency/coefficient of performance (COP) dominate their mean values. Their distributions show power law tails, however the exponents are not universal. Our study reveals that microscopic machines are not the microscopic equivalent of the macroscopic machines that we come across in our daily life. We find that there is no one to one correspondence between the performance of our system under engine protocol and its reverse.

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General Criterion for Harmonicity

Cited by 4 publications

References 20 publications

Phase transitions in persistent and run-and-tumble walks

Phase transitions in persistent and run-and-tumble walks

First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension

Anomalous Brownian refrigerator

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