Statistical physics and information theory for systems with local constraints

Doctoral Thesis

Systems with local constraints is a new finding in recent researches on complex systems. The heterogeneous spatial interactions and the temporal dependencies among those numerous units make it difficult to describe by traditional statistical physics.
These complex structures also make information storage and transmission in it is impossible to describe by the random variables with finite outcomes in the classical information theory. In this thesis, we use the statistical ensemble with local constraints to describe those complex systems with heterogeneous interactions and dependencies. This description also helps us find the new information-theoretical bounds in the systems with local constraints, even when the temporal dependencies among numerous units break the asymptotic equipartition property in the classical information theory.
Furthermore, we find that the breaking of ensemble equivalence generally exists in systems with local constraints even without the presence of...Show moreSystems with local constraints is a new finding in recent researches on complex systems. The heterogeneous spatial interactions and the temporal dependencies among those numerous units make it difficult to describe by traditional statistical physics.
These complex structures also make information storage and transmission in it is impossible to describe by the random variables with finite outcomes in the classical information theory. In this thesis, we use the statistical ensemble with local constraints to describe those complex systems with heterogeneous interactions and dependencies. This description also helps us find the new information-theoretical bounds in the systems with local constraints, even when the temporal dependencies among numerous units break the asymptotic equipartition property in the classical information theory.
Furthermore, we find that the breaking of ensemble equivalence generally exists in systems with local constraints even without the presence of phase transition, and this ensemble nonequivalence in the systems with local constraints without phase transition can be the same strong as the one that only appears on the boundary of phase transitions caused by the long-range interactions. We also find that this breaking of ensemble equivalence will affect the limit of information storage and transmission in systems with local constraints.
These results in this thesis extend our understanding of complex systems and information theory.
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Systems with local constraints

Ensemble nonequivalence

Information theory

Statistical physics