Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

The effect of osmolytes on protein fold stability at the single-molecule level

By pulling and releasing the tension on protein homomers with the Atomic Force Miscroscope (AFM) at different pulling speeds, dwell times and dwell distances, the observed force-response of the protein can be fitted with suitable theoretical models. In this respect we developed mathematical procedures and open-source computer codes for driving such experiments and fitting Bell’s model to experimental protein unfolding forces and protein folding frequencies. We applied the above techniques to the study of proteins GB1 (the B1 IgG-binding domain of protein G from Streptococcus) and I27 (a module of human cardiac titin) in aqueous solutions of protecting osmolytes such as dimethyl sulfoxide (DMSO), glycerol and trimethylamine N-oxide (TMAO). In order to get a molecular understanding of the experimental results we developed an Ising-like model for proteins that incorporates the osmophobic nature of their backbone. The model benefits from analytical thermodynamics and kinetics amenable to Monte-Carlo simulation. The prevailing view used to be that small protecting osmolytes bridge the separating beta-strands of proteins with mechanical resistance, presumably shifting the transition state to significantly higher distances that correlate with the molecular size of the osmolyte molecules. Our experiments showed instead that protecting osmolytes slow down protein unfolding and speed-up protein folding at physiological pH without shifting the protein transition state on the mechanical reaction coordinate. Together with the theoretical results of the Ising-model, our results lend support to the osmophobic theory according to which osmolyte stabilisation is a result of the preferential exclusion of the osmolyte molecules from the protein backbone. The results obtained during this thesis work have markedly improved our understanding of the strategy selected by Nature to strengthen protein stability in hostile environments, shifting the focus from hypothetical protein-osmolyte interactions to the more general mechanism based on the osmophobicity of the protein backbone.

Negativi di memoria. La rappresentazione del trauma nel romanzo del Novecento. Samuel Beckett, Georges Perec, Agota Kristof

Oggetto di questa tesi è l’analisi delle modalità di rappresentazione del trauma nel romanzo del Novecento e, in particolare, nelle opere di Samuel Beckett, Georges Perec e Agota Kristof. Fondamento dello studio sarà una disamina dei procedimenti linguistici e narrativi di rappresentazione del trauma nelle prose degli autori citati, al fine tracciare le linee di un’estetica in grado di descrivere le caratteristiche peculiari delle narrazioni in cui la dimensione antinarrativa della memoria traumatica assume il ruolo di principio estetico guida. L’analisi si soffermerà sulla cruciale relazione esistente, in tutti e tre gli autori, tra rappresentazione del trauma e sviluppo di strategie narrativi definibili come “denegative”. L’analisi dei testi letterari è condotta sulla base del corpus critico dei Trauma Studies, dell’ermeneutica della narrazione di stampo ricœuriano e della teoria del linguaggio psicoanalitica e affiancata, ove possibile, da uno studio filologico-genetico dei materiali d’autore. Alla luce di tali premesse, intendo rivalutare il carattere rappresentativo e testimoniale della letteratura del secolo scorso, in contrasto con la consuetudine a vedere nel romanzo novecentesco il trionfo dell’antimimesi e il declino del racconto. Dal momento che le narrazioni traumatiche si costruiscono intorno e attraverso i vuoti di linguaggio, la tesi è che siano proprio questi vuoti linguistici e narrativi (amnesie, acronie, afasie, lapsus, omissioni e mancanze ancora più sofisticate come nel caso di Perec) a rappresentare, in modo mimetico, la realtà apparentemente inaccessibile del trauma. Si tenterà di dimostrare come questi nuovi canoni di rappresentazione non denuncino l’impossibilità del racconto, bensì una sfida al silenzio, celata in più sottili e complesse convenzioni narrative, le quali mantengono un rapporto di filiazione indiretto − per una via che potremmo definire denegativa − con quelle del romanzo tradizionale.