Drazin-Inverse and heat capacity for driven random walks on the ring

Irene, Maes,; Faezeh, Khodabandehlou,

doi:10.48550/arxiv.2204.04974

Cited by 7 publications

(7 citation statements)

References 13 publications

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“…shown in Fig. 1 in [26], and to the findings in [34] for active random walks on a ring. The appearance of a Schottky-like anomaly [35] for small enough v indeed shows the presence of a single energy scale E 0 in the potential.…”

Section: B Run-and-tumble In a Periodic Potentialsupporting

confidence: 71%

Calorimetry for active systems

Dolai¹,

Maes²,

Netočný³

2022

Preprint

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Perturbing the temperature, the heat capacity measures the excess heat in addition to the steady ever-existing dissipation. Simulating AC-calorimetry, we numerically evaluate the heat capacity for run-and-tumble particles in double-well and periodic potentials. Low-temperature Schottky-like peaks show the role of activity and indicate shape transitions, while regimes of negative heat capacity appear at higher propulsion speeds.

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Section: B Run-and-tumble In a Periodic Potentialsupporting

confidence: 71%

Calorimetry for active systems

Dolai¹,

Maes²,

Netočný³

2022

Preprint

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“…Here we present the upshot of those results as concerns the computation of (VI.3) and hence of (VI.2). Applications are found in [15,32].…”

Section: A Matrix-forest Theoremmentioning

confidence: 99%

“…We have in mind the arborification of trajectories as suggested in e.g. [13][14][15][16]. To review and extend these techniques is the subject of the present paper.…”

Section: Introductionmentioning

confidence: 99%

Trees and Forests for Nonequilibrium Purposes: An Introduction to Graphical Representations

2022

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Using local detailed balance we rewrite the Kirchhoff formula for stationary distributions of Markov jump processes in terms of a physically interpretable treeensemble. We use that arborification of path-space integration to derive a McLennantree characterization close to equilibrium, as well as to obtain response formula for the stationary distribution in the asymptotic regime of large driving. Graphical expressions of currents and dynamical activity are obtained, allowing the study of various asymptotic regimes. Finally, we present how the matrix-forest theorem gives a representation of quasi-potentials, as used e.g. for computing excess work and heat in nonequilibrium thermal physics. For pedagogical purposes, we add simple examples to illustrate and explain the various graphical elements.

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“…We collect here mathematical ingredients, essential for the derivation of the nonequilibrium Nernst heat theorem. More details make the subject of a separate paper [32], in particular for the derivation of the graphical representations starting with the matrix-forest theorem [33][34][35]. For an introduction to graphical methods for nonequilibrium purposes, see [36].…”

Section: Appendix A: Mathematical Ingredientsmentioning

confidence: 99%

A Nernst heat theorem for nonequilibrium jump processes

Faezeh¹,

Maes²,

Netočný³

2022

Preprint

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We generalize a version of the Third Law of Thermodynamics to nonequilibrium processes described as Markov jump dynamics on a finite connected graph. In addition to the stationary heat flux, after a small change in an external parameter, an excess heat flows into the thermal bath at temperature T during relaxation. We state conditions under which that excess heat and the nonequilibrium heat capacity vanish as T ↓ 0. The interpretation is that typical relaxation paths towards dominant states do not dramatically differ from each other in their dissipated heat.

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Drazin-Inverse and heat capacity for driven random walks on the ring

Cited by 7 publications

References 13 publications

Calorimetry for active systems

Calorimetry for active systems

Trees and Forests for Nonequilibrium Purposes: An Introduction to Graphical Representations

A Nernst heat theorem for nonequilibrium jump processes

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