We consider the problem of building a continuous stochastic model, i.e., a Langevin or Fokker-Planck equation, through a well-controlled coarse-graining procedure. Such a method usually involves the elimination of the fast degrees of freedom of the “bath” to which the particle is coupled. Specifically, we look into the general case where the bath may be at negative temperatures, as found, for instance, in models and experiments with bounded effective kinetic energy. Here, we generalize previous studies by considering the case in which the coarse graining leads to (i) a renormalization of the potential felt by the particle, and (ii) spatially dependent viscosity and diffusivity. In addition, a particular relevant example is provided, where the bath is a spin system and a sort of phase transition takes place when going from positive to negative temperatures. A Chapman-Enskog-like expansion allows us to rigorously derive the Fokker-Planck equation from the microscopic dynamics. Our theoretical predictions show excellent agreement with numerical simulations.

Derivation of a Langevin equation in a system with multiple scales: The case of negative temperatures / Baldovin, Marco; Vulpiani, Angelo; Puglisi, Andrea; PRADOS MONTANO, Antonio. - In: PHYSICAL REVIEW. E. - ISSN 2470-0045. - 99:6(2019). [10.1103/PhysRevE.99.060101]

Derivation of a Langevin equation in a system with multiple scales: The case of negative temperatures

Baldovin, Marco;Vulpiani, Angelo;Puglisi, Andrea;PRADOS MONTANO, ANTONIO
2019

Abstract

We consider the problem of building a continuous stochastic model, i.e., a Langevin or Fokker-Planck equation, through a well-controlled coarse-graining procedure. Such a method usually involves the elimination of the fast degrees of freedom of the “bath” to which the particle is coupled. Specifically, we look into the general case where the bath may be at negative temperatures, as found, for instance, in models and experiments with bounded effective kinetic energy. Here, we generalize previous studies by considering the case in which the coarse graining leads to (i) a renormalization of the potential felt by the particle, and (ii) spatially dependent viscosity and diffusivity. In addition, a particular relevant example is provided, where the bath is a spin system and a sort of phase transition takes place when going from positive to negative temperatures. A Chapman-Enskog-like expansion allows us to rigorously derive the Fokker-Planck equation from the microscopic dynamics. Our theoretical predictions show excellent agreement with numerical simulations.
2019
Multiple-scale dynamics; Langevin equation; negatve temperatures
01 Pubblicazione su rivista::01a Articolo in rivista
Derivation of a Langevin equation in a system with multiple scales: The case of negative temperatures / Baldovin, Marco; Vulpiani, Angelo; Puglisi, Andrea; PRADOS MONTANO, Antonio. - In: PHYSICAL REVIEW. E. - ISSN 2470-0045. - 99:6(2019). [10.1103/PhysRevE.99.060101]
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Note: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.99.060101
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1283453
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