Nonequilibrium work theorems, such as the Jarzynski equality and the Crooks fluctuation theorem, allow one to use nonequilibrium measurements to determine equilibrium free energies. For example, it has been demonstrated that the Crooks fluctuation theorem can be used to determine RNA folding energies. We used single-molecule manipulation with an atomic force microscope to measure the work done on poly(dA) as it was stretched and relaxed. This single-stranded nucleic acid exhibits unique base-stacking transitions in its force-extension curve due to the strong interactions among A bases, as well as multiple pathways. Here we showed that free energy curves can be determined by using the Crooks fluctuation theorem. The nonequilibrium work theorem can be used to determine free energy curves even when there are multiple pathways.

Nonequilibrium work theorems, such as the Jarzynski equality and the Crooks fluctuation theorem, allow one to use nonequilibrium measurements to determine equilibrium free energies. For example, it has been demonstrated that the Crooks fluctuation theorem can be used to determine RNA folding energies. We used single-molecule manipulation with an atomic force microscope to measure the work done on poly(dA) as it was stretched and relaxed. This single-stranded nucleic acid exhibits unique base-stacking transitions in its force-extension curve due to the strong interactions among A bases, as well as multiple pathways. Here we showed that free energy curves can be determined by using the Crooks fluctuation theorem. The nonequilibrium work theorem can be used to determine free energy curves even when there are multiple pathways.

Nonequilibrium work theorems, such as the Jarzynski equality and the Crooks fluctuation theorem, allow one to use nonequilibrium measurements to determine equilibrium free energies. For example, it has been demonstrated that the Crooks fluctuation theorem can be used to determine RNA folding energies. We used single-molecule manipulation with an atomic force microscope to measure the work done on poly(dA) as it was stretched and relaxed. This single-stranded nucleic acid exhibits unique base-stacking transitions in its force-extension curve due to the strong interactions among A bases, as well as multiple pathways. Here we showed that free energy curves can be determined by using the Crooks fluctuation theorem. The nonequilibrium work theorem can be used to determine free energy curves even when there are multiple pathways.

Nonequilibrium work theorems, such as the Jarzynski equality and the Crooks fluctuation theorem, allow one to use nonequilibrium measurements to determine equilibrium free energies. For example, it has been demonstrated that the Crooks fluctuation theorem can be used to determine RNA folding energies. We used single-molecule manipulation with an atomic force microscope to measure the work done on poly(dA) as it was stretched and relaxed. This single-stranded nucleic acid exhibits unique base-stacking transitions in its force-extension curve due to the strong interactions among A bases, as well as multiple pathways. Here we showed that free energy curves can be determined by using the Crooks fluctuation theorem. The nonequilibrium work theorem can be used to determine free energy curves even when there are multiple pathways.

The weather dynamics are significantly determined by the motion of the atmosphere and the ocean. This motion is often turbulent, characterized by fluctuations of the flow velocity over wide spatial and temporal scales. This fact, besides limited observability and inaccurate models, impedes the predictability of quantities such as the velocity of winds, which are relevant for the everyday life. One is always interested in improving such predictions - by employing better models or obtaining more information about the system. The Crooks fluctuation theorem is a relation from nonequilibrium thermodynamics, which has its typical applications in nanoscale systems. It quantifies the distribution of imposed work in a process, where the system is pushed out of thermal equilibrium. This distribution is broadened due to the fluctuations of the microscopic degrees of freedom in the system. The fluctuations of the velocity field in turbulent flow suggest the derivation of an analogy of Crooks' theorem for this macroscopic system. The knowledge about the validity of such a relation is additional information, which one in reverse could use to improve predictions about the system. In this thesis both issues are addressed: the derivation of the theorem, and the improvement of predictions. We illustrate the application of Crooks' theorem to hydrodynamic flow within a model of a two-dimensional inviscid and incompressible fluid field, when pushed out of dynamical equilibrium. The flow on a rectangular domain is approximated by the two-dimensional vorticity equation with spectral truncation. In this setting, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, kinetic energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. This is interpreted as doing work to the system. Evolving along a forward and its corresponding backward process, we find that the distributions of the work performed in these processes satisfy the Crooks relation with parameters derived from the canonical ensembles. We address the issue of prediction in this thesis in a concrete setting: There are examples where the distributions of a variable in the forward and the backward process collapse into one, hence Crooks' theorem relates the distribution of one variable with itself. For a finite data set drawn from such a distribution, we are interested in an estimate of this variable to exceed a certain threshold. We demonstrate that, using the knowledge about Crooks' relation, forecast schemes can be proposed which improve compared to a pure frequency estimate on the data set. The findings are illustrated in three examples, studies of parameters such as exceedance threshold and data set size are presented.

The weather dynamics are significantly determined by the motion of the atmosphere and the ocean. This motion is often turbulent, characterized by fluctuations of the flow velocity over wide spatial and temporal scales. This fact, besides limited observability and inaccurate models, impedes the predictability of quantities such as the velocity of winds, which are relevant for the everyday life. One is always interested in improving such predictions - by employing better models or obtaining more information about the system. The Crooks fluctuation theorem is a relation from nonequilibrium thermodynamics, which has its typical applications in nanoscale systems. It quantifies the distribution of imposed work in a process, where the system is pushed out of thermal equilibrium. This distribution is broadened due to the fluctuations of the microscopic degrees of freedom in the system. The fluctuations of the velocity field in turbulent flow suggest the derivation of an analogy of Crooks' theorem for this macroscopic system. The knowledge about the validity of such a relation is additional information, which one in reverse could use to improve predictions about the system. In this thesis both issues are addressed: the derivation of the theorem, and the improvement of predictions. We illustrate the application of Crooks' theorem to hydrodynamic flow within a model of a two-dimensional inviscid and incompressible fluid field, when pushed out of dynamical equilibrium. The flow on a rectangular domain is approximated by the two-dimensional vorticity equation with spectral truncation. In this setting, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, kinetic energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. This is interpreted as doing work to the system. Evolving along a forward and its corresponding backward process, we find that the distributions of the work performed in these processes satisfy the Crooks relation with parameters derived from the canonical ensembles. We address the issue of prediction in this thesis in a concrete setting: There are examples where the distributions of a variable in the forward and the backward process collapse into one, hence Crooks' theorem relates the distribution of one variable with itself. For a finite data set drawn from such a distribution, we are interested in an estimate of this variable to exceed a certain threshold. We demonstrate that, using the knowledge about Crooks' relation, forecast schemes can be proposed which improve compared to a pure frequency estimate on the data set. The findings are illustrated in three examples, studies of parameters such as exceedance threshold and data set size are presented.

A proposta deste trabalho é a de discutir aspectos do som da trompa, que está profundamente enraizado no instrumento histórico, anterior ao século XIX. É o som da trompa que inspira os músicos, atrai os ouvintes e estimula os compositores. É seu som que mantém o músico estudando por horas para adquirir as habilidades necessárias para tocar bem. Nos ouvintes, o som da trompa evoca heroísmo e nobreza, saudosismo e romantismo e, por décadas, foi a voz básica destes sentimentos em filmes e trilhas sonoras. Os compositores têm mantido uma relação sempre cambiante com este instrumento que, por sua vez, continua a se modificar, e as inovações que eles propuseram afetaram diretamente o som do instrumento. Esta pesquisa irá explorar as técnicas que os trompistas têm à disposição para dar colorido ao som do instrumento. A maioria destas tem suas raízes na execução da trompa natural e esta é a justificativa para a abordagem utilizada neste trabalho: aplicar as técnicas da trompa natural na execução da trompa de válvulas. O timbre da trompa natural é bastante afetado pela posição da mão. A sonoridade resultante pode ficar abafada, emudecida, metálica, cálida e rica ou aberta e brilhante. A ornamentação em forma de trinados labiais, grupetos e mordentes é um resultado da habilidade do executante, assim como arpejar fácil e fluentemente ao longo da extensão do instrumento, é também um exemplo de habilidade técnica. Esta fluência apresenta-se como um aspecto da cor da tonalidade. A afinação, seja ela diatônica, justa, em quartos de tom ou seguindo a série harmônica naturais, também enfeita a cor do som. Na trompa, a afinação seguindo a série harmônica é obtida simplesmente tocando-se as notas naturais do instrumento. Como músico de orquestra, acredito que o posicionamento correta da mão e o treinamento da flexibilidade na trompa natural beneficiaram-me na obtenção das cores e no balanço desejados na música tocada em meu instrumento de válvulas. Enquanto solista e músico de câmara, os benefícios e novos usos dessas técnicas foram ainda mais evidentes. Este trabalho pretende então demonstrar, pela provisão de exemplos da literatura e da prática profissional, como as técnicas da trompa natural podem melhorar a performance da trompa de válvulas moderna. / The purpose of this document is to discuss aspects of horn sound deeply rooted in the pre-19th-century historical instrument. It is the sound of the horn that inspires players, draws listeners, and stimulates composers. Sound keeps the performer practicing for hours to learn the skills required to play well. To listeners, the horns sound evokes heroism and nobility, wistfulness and romance; for decades it has been an essential voice for such qualities in motion picture sound tracks. Composers have maintained an ever-changing relationship with an instrument that continues to evolve; their innovations directly affect the sound of the horn. This inquiry will explore techniques that horn players could use to color the horns sound. Most of these techniques have their roots in natural horn performance, thus the reason for the manner of my approach: applying natural horn techniques to modern valved horn performance practice. Sound colors are not only characterized by timbre, but also through facility and intonation. Natural horn timbres are largely affected by hand position. The resulting sonority can be muffled, muted, brassy, warm and rich, or open and bright. The players ability to provide ornamentation through lip trills, turns, and mordents is a result of his or her facility. The ability to arpeggiate fluently and easily throughout the range of the instrument is another example of facile technique. This fluency exhibits itself as aspects of tone color. Intonation, whether it be diatonic, just, quartertone or natural harmonic, also colors sound. For the horn, natural harmonic intonation is simply achieved by playing the unadjusted notes of the harmonic series. As an orchestral player, I find that the right hand and flexibility training on my natural horn has been of great benefit in creating, on my valved horn, the colors and balance desired in the music. As a soloist, orchestral and chamber player, the benefits and new uses of these techniques are even more pronounced. This document is designed to demonstrate, by providing examples from the literature and professional practice, how natural horn skills can enhance modern valved horn performance.

A proposta deste trabalho é a de discutir aspectos do som da trompa, que está profundamente enraizado no instrumento histórico, anterior ao século XIX. É o som da trompa que inspira os músicos, atrai os ouvintes e estimula os compositores. É seu som que mantém o músico estudando por horas para adquirir as habilidades necessárias para tocar bem. Nos ouvintes, o som da trompa evoca heroísmo e nobreza, saudosismo e romantismo e, por décadas, foi a voz básica destes sentimentos em filmes e trilhas sonoras. Os compositores têm mantido uma relação sempre cambiante com este instrumento que, por sua vez, continua a se modificar, e as inovações que eles propuseram afetaram diretamente o som do instrumento. Esta pesquisa irá explorar as técnicas que os trompistas têm à disposição para dar colorido ao som do instrumento. A maioria destas tem suas raízes na execução da trompa natural e esta é a justificativa para a abordagem utilizada neste trabalho: aplicar as técnicas da trompa natural na execução da trompa de válvulas. O timbre da trompa natural é bastante afetado pela posição da mão. A sonoridade resultante pode ficar abafada, emudecida, metálica, cálida e rica ou aberta e brilhante. A ornamentação em forma de trinados labiais, grupetos e mordentes é um resultado da habilidade do executante, assim como arpejar fácil e fluentemente ao longo da extensão do instrumento, é também um exemplo de habilidade técnica. Esta fluência apresenta-se como um aspecto da cor da tonalidade. A afinação, seja ela diatônica, justa, em quartos de tom ou seguindo a série harmônica naturais, também enfeita a cor do som. Na trompa, a afinação seguindo a série harmônica é obtida simplesmente tocando-se as notas naturais do instrumento. Como músico de orquestra, acredito que o posicionamento correta da mão e o treinamento da flexibilidade na trompa natural beneficiaram-me na obtenção das cores e no balanço desejados na música tocada em meu instrumento de válvulas. Enquanto solista e músico de câmara, os benefícios e novos usos dessas técnicas foram ainda mais evidentes. Este trabalho pretende então demonstrar, pela provisão de exemplos da literatura e da prática profissional, como as técnicas da trompa natural podem melhorar a performance da trompa de válvulas moderna. / The purpose of this document is to discuss aspects of horn sound deeply rooted in the pre-19th-century historical instrument. It is the sound of the horn that inspires players, draws listeners, and stimulates composers. Sound keeps the performer practicing for hours to learn the skills required to play well. To listeners, the horns sound evokes heroism and nobility, wistfulness and romance; for decades it has been an essential voice for such qualities in motion picture sound tracks. Composers have maintained an ever-changing relationship with an instrument that continues to evolve; their innovations directly affect the sound of the horn. This inquiry will explore techniques that horn players could use to color the horns sound. Most of these techniques have their roots in natural horn performance, thus the reason for the manner of my approach: applying natural horn techniques to modern valved horn performance practice. Sound colors are not only characterized by timbre, but also through facility and intonation. Natural horn timbres are largely affected by hand position. The resulting sonority can be muffled, muted, brassy, warm and rich, or open and bright. The players ability to provide ornamentation through lip trills, turns, and mordents is a result of his or her facility. The ability to arpeggiate fluently and easily throughout the range of the instrument is another example of facile technique. This fluency exhibits itself as aspects of tone color. Intonation, whether it be diatonic, just, quartertone or natural harmonic, also colors sound. For the horn, natural harmonic intonation is simply achieved by playing the unadjusted notes of the harmonic series. As an orchestral player, I find that the right hand and flexibility training on my natural horn has been of great benefit in creating, on my valved horn, the colors and balance desired in the music. As a soloist, orchestral and chamber player, the benefits and new uses of these techniques are even more pronounced. This document is designed to demonstrate, by providing examples from the literature and professional practice, how natural horn skills can enhance modern valved horn performance.