Non-equilibrium statistical mechanics of complex systems
Non-equilibrium statistical mechanics of complex systems
Disciplines
Computer Sciences (10%); Mathematics (25%); Physics, Astronomy (65%)
Keywords
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Complex Non-Extensive Systems,
Generalized Entropy,
Scaling,
Stochsatic Thermodynamics,
Non-Equilibrium,
Emergent Structures
Many complex systems are stochastic systems that can be described with methods from statistical physics once the methods take into account the complex structure of these systems. One difficulty with complex systems is that with increasing size (number of degrees of freedom), they often show a non-exponential growth of phase space volume. It is caused either by the presence of inherent correlations in the system caused, e.g., by the long-range interactions (as for quantum entanglement or gravitating objects), or by the emergence of higher-order structures that appear with increasing size of the system. It leads to a number of sometimes unexpected thermodynamical properties of complex systems. While sub- exponential, i.e., correlated, systems have been studied intensively in the past decades, so far, super-exponential ones have not received attention. These include important stochastic systems that can form structures. One can find examples of these systems in chemistry (atoms forming molecules), biology and biochemistry (micelles and polymers), soft matter (self- assembly), or even in social systems (emergence of social groups). To date, there is limited knowledge on how to understand their statistical and thermodynamical properties, particularly how to adequately describe their non-equilibrium states that play a role in small systems. The main aim of this project is to establish a systematic classification scheme of complex systems of this kind with a focus on their statistical properties out-of-equilibrium. We further want to contribute to a consistent thermodynamic framework for such systems. Finally, we aim to compare the theoretical results with real-world examples, such as small chemical reaction networks. To this end, we will complement our analytical approaches with computer simulations.
Research Output
- 16 Citations
- 11 Publications
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2022
Title Geometric Structures Induced by Deformations of the Legendre Transform DOI 10.48550/arxiv.2203.13673 Type Preprint Author Morales P -
2023
Title Homophily-Based Social Group Formation in a Spin Glass Self-Assembly Framework DOI 10.1103/physrevlett.130.057401 Type Journal Article Author Korbel J Journal Physical Review Letters Pages 057401 Link Publication -
2023
Title Thermodynamics of exponential Kolmogorov–Nagumo averages DOI 10.1088/1367-2630/ace4eb Type Journal Article Author Morales P Journal New Journal of Physics Pages 073011 Link Publication -
2023
Title Thermodynamics of exponential Kolmogorov-Nagumo averages DOI 10.48550/arxiv.2302.06959 Type Preprint Author Morales P -
2023
Title Geometric Structures Induced by Deformations of the Legendre Transform DOI 10.3390/e25040678 Type Journal Article Author Morales P Journal Entropy Pages 678 Link Publication -
2023
Title Equivalence of information production and generalised entropies in complex processes DOI 10.1371/journal.pone.0290695 Type Journal Article Author Hanel R Journal PLOS ONE Link Publication -
2022
Title Equivalence of information production and generalized entropies in complex processes DOI 10.48550/arxiv.2208.06201 Type Preprint Author Hanel R -
2022
Title Nonequilibrium thermodynamics of uncertain stochastic processes DOI 10.48550/arxiv.2210.05249 Type Preprint Author Korbel J -
2024
Title Diversity and ecotones in a model ecosystems of sessile species DOI 10.1103/physreve.109.024309 Type Journal Article Author Hofer M Journal Physical Review E Pages 024309 -
2024
Title Nonequilibrium thermodynamics of uncertain stochastic processes DOI 10.1103/physrevresearch.6.013021 Type Journal Article Author Korbel J Journal Physical Review Research Pages 013021 Link Publication -
2022
Title Homophily-based social group formation in a spin-glass self-assembly framework DOI 10.48550/arxiv.2211.12210 Type Preprint Author Korbel J