Manifestations of Memory in Time- and Ensemble-Average Statistical Mechanics of Low-dimensional Physical Observables
von Alessio Lapolla
Datum der mündl. Prüfung:2021-05-31
Erschienen:2021-06-07
Betreuer:Dr. Aljaz Godec
Gutachter:Dr. Aljaz Godec
Gutachter:Prof. Dr. Krueger Matthias
Dateien
Name:thesis.pdf
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Format:PDF
Description:PhD thesis
Zusammenfassung
Englisch
The study of stochastic processes plays a very important role in our current understanding of Statistical Physics, in particular many results from this field have found successful applications in biological, socio-economics and condensed matter systems. An important feature of stochastic process is the presence, or absence, of memory, i.e.: does the state of the system at a certain time depends on its history or not? In many physically relevant scenarios the answer is yes. Henceforth in the articles collected in this thesis we, at least partially, constructed a theory able to describe and compute relevant properties of processes with memory. This goal has been achieved in two ways: consid- ering time-averaged observables and then obtaining explicit results for the respective expectation moments, and studying how a dimensionality reduc- tion procedure acting on a multi-dimensional memoryless system produces a resulting process displaying memory effects. Finally the two approaches have been combined as well. We used the theory so developed to analyze classical exactly solvable many-body systems in Statistical Mechanics: the single file and the Gaussian network models. We also applied our analysis to trajectories derived from experimental time-series and Molecular Dynamics simulations. We used the tools we developed to elucidate properties of relaxation processes towards equilibrium and to investigate the memory origin of the breaking of time- translation invariance.
Keywords: Statistical Mechanics; Non Markovian processes; projection operators