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ETDs @PUC-Rio
Estatística
Título: NONLINEAR BROWNIAN MACHINES
Autor: LUCIANNO AUGUSTO CODDATO ANTUNES E DEFAVERI
Colaborador(es): WELLES ANTONIO MARTINEZ MORGADO - Orientador
SILVIO MANUEL DUARTE QUEIROS - Coorientador
Catalogação: 06/ABR/2021 Língua(s): ENGLISH - UNITED STATES
Tipo: TEXT Subtipo: THESIS
Notas: [pt] Todos os dados constantes dos documentos são de inteira responsabilidade de seus autores. Os dados utilizados nas descrições dos documentos estão em conformidade com os sistemas da administração da PUC-Rio.
[en] All data contained in the documents are the sole responsibility of the authors. The data used in the descriptions of the documents are in conformity with the systems of the administration of PUC-Rio.
Referência(s): [pt] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=52053&idi=1
[en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=52053&idi=2
DOI: https://doi.org/10.17771/PUCRio.acad.52053
Resumo:
In the recent decade we have seen great interest in the physics of single particle microscopic engines. Not only we have seen advances in the theoretical understanding of how such systems behave but also, thanks to the advanced level of microscopic manipulations, we are capable of reproducing these systems in experimental situations. The literature is quite large when considering machines where a single particle is subjected to a harmonic potential where we can control the stiffness and in contact with a heat bath of controllable temperature. Motivated by these outstanding results, we have decided to investigate an alternative mechanism to studying machines. We propose and investigate a setup where a single particle with an internal nonlinear potential in contact with a heat bath of temperature T that we can control, then we introduce an external quadratic potential centered in a position L which will break the internal symmetry and create a direction where the particle can fluctuate to with greater ease. We can use this symmetry breaking to convert heat into work. Starting with a nonlinear correction to a predominantly linear internal potential, we use perturbation theory to solve the Langevin equation of the system up to the first order o k4 and obtain the expected work and absorbed heat. We then relax the restriction of a small nonlinear by imposing that the cycle periods are so large that, at least to some extent, the system can be considered in equilibrium with the heat bath. Using classical statistical mechanics we obtain results for a wider range of nonlinearities. Since the key component of our machines is the asymmetry, we extend the internal potential to the more general but not always analytical form V(i)(x) proportional to (x) raised to alpha which we label alpha-typepotential. Using primarily numerical techniques investigate its properties and outputs for different values of alpha. Lastly we study the Carnot cycle by replacing the adiabatical branches with isentropic ones, investigating the relationship between alpha and the isentropic trajectories. All results are compared with numerical simulations.
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