This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The book contains numerous illustrations throughout and it will interest both mathematicians and physicists.
Se l’Informe è un carattere della nostra epoca, è indispensabile ripensare gli strumenti con cui descriviamo e trasformiamo la realtà. Come potrebbero mutare i nostri paradigmi se assumessimo l’Informe come strumento critico? Il ruolo operativo dell’Informe, proposto da Georges Bataille, permette di dare senso a molte pratiche di trasformazione del mondo. “Assemblaggi” è costruito come un montaggio di testi su autori di diverse epoche. La descrizione e il commento delineano un percorso che indaga la potenza plastica e critica dell’Informe come apertura all’indeterminato. L’idea di un’Architettura geologica interroga le pieghe della Terra e dispiega una pratica del “maifinito” come nodo di congiunzione tra tempi e mondi diversi. Mettere in forma la tensione tra le cose costituisce il compito di un’Architettura terrestre per immaginare nuove alleanze capaci di generare futuri.
Recent experimental evidence about the possibility of "absolute negative temperature" states in physical systems has triggered a stimulating debate about the consistency of such a concept from the point of view of Statistical Mechanics. It is not clear whether the usual results of this field can be safely extended to negative-temperature states; some authors even propose fundamental modifications to the Statistical Mechanics formalism, starting with the very definition of entropy, in order to avoid the occurrence of negative values of the temperature tout-court. The research presented in this thesis aims to shed some light on this controversial topic. To this end, a particular class of Hamiltonian systems with bounded kinetic terms, which can assume negative temperature, is extensively studied, both analytically and numerically. Equilibrium and out-of-equilibrium properties of this kind of system are investigated, reinforcing the overall picture that the introduction of negative temperature does not lead to any contradiction or paradox.
This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The book contains numerous illustrations throughout and it will interest both mathematicians and physicists.
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