Large deviations for quadratic functionals of stable Gauss-Markov chains and entropy production

Zamparo, Marco; Semeraro, Massimiliano

doi:10.48550/arxiv.2204.08059

Cited by 2 publications

(2 citation statements)

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“…A large deviation theory beyond Poissonian resetting allows to appreciate the emergence of singularities in the graph of their rate functions, which are interpreted as dynamical phase transitions. Dynamical phase transitions have been already documented for time-averaged quantities such as the heat exchanged after a quench [27,28], the heat exchanged between two thermal walls [29,30], the active work in active matter [31], the total displacement of random walks [32][33][34][35], occupation times of a Brownian particle [36,37], and the entropy production [38][39][40][41][42]. Physicists often invoke the Gärtner-Ellis theorem to justify their calculations that lead to dynamical phase transitions, although it is necessary for a dynamical phase transition to occur that the hypotheses of that theorem are violated.…”

Section: Introductionmentioning

confidence: 99%

Statistical fluctuations under resetting: rigorous results

Zamparo¹

2022

J. Phys. A: Math. Theor.

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In this paper we investigate the normal and the large fluctuations of additive functionals associated with a stochastic process under a general non-Poissonian resetting mechanism. Cumulative functionals of regenerative processes are very close to renewal-reward processes and inherit most of the properties of the latter. Here we review and use the classical law of large numbers and central limit theorem for renewal-reward processes to obtain same theorems for additive functionals of a stochastic process under resetting. Then, we establish large deviation principles for these functionals by illustrating and applying a large deviation theory for renewal-reward processes that has been recently developed by the author. We discuss applications of the general results to the positive occupation time, the area, and the absolute area of the reset Brownian motion. While introducing advanced tools from renewal theory, we demonstrate that a rich phenomenology accounting for dynamical phase transitions emerges when one goes beyond Poissonian resetting.

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Section: Introductionmentioning

confidence: 99%

Statistical fluctuations under resetting: rigorous results

Zamparo¹

2022

J. Phys. A: Math. Theor.

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“…A large deviation theory beyond Poissonian resetting allows us to appreciate the emergence of singularities in the graph of their rate functions, which are interpreted as dynamical phase transitions. Dynamical phase transitions have been already documented for time-averaged quantities such as the heat exchanged after a quench [37,38], the active work in active matter [39], the total displacement of random walks [40][41][42][43], occupation times of a Brownian particle [44,45], and the entropy production [46][47][48][49][50]. Physicists often invoke the Gärtner-Ellis theorem to justify their calculations that lead to dynamical phase transitions, although it is necessary for a dynamical phase transition to occur that the hypotheses of that theorem are violated.…”

Section: Introductionmentioning

confidence: 99%

Statistical fluctuations under resetting: rigorous results

Zamparo¹

2022

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In this paper we investigate the normal and the large fluctuations of additive functionals of the Brownian motion under a general non-Poissonian resetting mechanism. Cumulative functionals of regenerative processes are very close to renewal-reward processes and inherit most of the properties of the latter. Here we review and use the classical law of large numbers and central limit theorem for renewal-reward processes to obtain same theorems for additive functionals of the reset Brownian motion. Then, we establish large deviation principles for these functionals by illustrating and applying a large deviation theory for renewal-reward processes that has been recently developed by the author. We discuss applications of the general results to the positive occupation time, the area, and the absolute area. While introducing advanced tools from renewal theory, we demonstrate that a rich phenomenology accounting for dynamical phase transitions emerges when one goes beyond Poissonian resetting.

show abstract

Large deviations for quadratic functionals of stable Gauss-Markov chains and entropy production

Cited by 2 publications

References 32 publications

Statistical fluctuations under resetting: rigorous results

Statistical fluctuations under resetting: rigorous results

Statistical fluctuations under resetting: rigorous results

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