Fluctuation-Response Theory of Non-Equilibrium Complex Fluids
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arXiv
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| Format: | Preprint |
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2025
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| author | Takaki, Ryota Jülicher, Frank |
| author_facet | Takaki, Ryota Jülicher, Frank |
| contents | A fundamental challenge in soft matter physics is to describe materials, such as the living cytoplasm and tissues, that are simultaneously active, chemically driven, and exhibit long-lasting memory of mechanical stresses. Here, we construct a generalized hydrodynamic framework at finite wavevectors and frequencies that can be applicable to non-equilibrium fluids with memory. Our approach is based on a non-equilibrium linear response relation in a steady state using correlation function identities and is distinct from the Mori-Zwanzig projection-operator formalism. This approach provides a framework to derive transport coefficients from correlation functions in non-equilibrium systems, extending the equilibrium Green-Kubo relations to non-equilibrium steady states. As a corollary, we obtain a non-equilibrium fluctuation-response relation for non-Markovian dynamics, which does not rely on specific models. Applying our theory to chemically driven active fluids reveals Active Viscoelastic Memory, whereby chemical reaction cycles renormalize the system's viscous response. We find that this active viscoelastic memory can produce negative storage and loss moduli at finite frequencies, a behavior absent in ordinary viscoelastic fluids. Our theory extends equilibrium rheology to materials far from equilibrium and reveals how non-equilibrium driving generates rheological features that are absent in equilibrium fluids. Our first-principles framework provides a general basis for understanding memory-dependent dynamics across a wide range of biological and synthetic active systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_15559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fluctuation-Response Theory of Non-Equilibrium Complex Fluids Takaki, Ryota Jülicher, Frank Soft Condensed Matter Statistical Mechanics A fundamental challenge in soft matter physics is to describe materials, such as the living cytoplasm and tissues, that are simultaneously active, chemically driven, and exhibit long-lasting memory of mechanical stresses. Here, we construct a generalized hydrodynamic framework at finite wavevectors and frequencies that can be applicable to non-equilibrium fluids with memory. Our approach is based on a non-equilibrium linear response relation in a steady state using correlation function identities and is distinct from the Mori-Zwanzig projection-operator formalism. This approach provides a framework to derive transport coefficients from correlation functions in non-equilibrium systems, extending the equilibrium Green-Kubo relations to non-equilibrium steady states. As a corollary, we obtain a non-equilibrium fluctuation-response relation for non-Markovian dynamics, which does not rely on specific models. Applying our theory to chemically driven active fluids reveals Active Viscoelastic Memory, whereby chemical reaction cycles renormalize the system's viscous response. We find that this active viscoelastic memory can produce negative storage and loss moduli at finite frequencies, a behavior absent in ordinary viscoelastic fluids. Our theory extends equilibrium rheology to materials far from equilibrium and reveals how non-equilibrium driving generates rheological features that are absent in equilibrium fluids. Our first-principles framework provides a general basis for understanding memory-dependent dynamics across a wide range of biological and synthetic active systems. |
| title | Fluctuation-Response Theory of Non-Equilibrium Complex Fluids |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2510.15559 |