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Das S, Green JR. Maximum speed of dissipation. Phys Rev E 2024; 109:L052104. [PMID: 38907451 DOI: 10.1103/physreve.109.l052104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 04/01/2024] [Indexed: 06/24/2024]
Abstract
We derive statistical-mechanical speed limits on dissipation from the classical, chaotic dynamics of many-particle systems. In one, the rate of irreversible entropy production in the environment is the maximum speed of a deterministic system out of equilibrium, S[over ¯]_{e}/k_{B}≥1/2Δt, and its inverse is the minimum time to execute the process, Δt≥k_{B}/2S[over ¯]_{e}. Starting with deterministic fluctuation theorems, we show there is a corresponding class of speed limits for physical observables measuring dissipation rates. For example, in many-particle systems interacting with a deterministic thermostat, there is a trade-off between the time to evolve between states and the heat flux, Q[over ¯]Δt≥k_{B}T/2. These bounds constrain the relationship between dissipation and time during nonstationary processes, including transient excursions from steady states.
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Affiliation(s)
- Swetamber Das
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA and Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA and Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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Sahbani M, Das S, Green JR. Classical Fisher information for differentiable dynamical systems. CHAOS (WOODBURY, N.Y.) 2023; 33:103139. [PMID: 37889952 DOI: 10.1063/5.0165484] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Accepted: 10/04/2023] [Indexed: 10/29/2023]
Abstract
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a form of uncertainty. Infinitesimal perturbations to the initial conditions can grow exponentially in time, a signature of deterministic chaos. As a measure of this uncertainty, we introduce another classical information, specifically for the deterministic dynamics of isolated, closed, or open classical systems not subject to noise. This classical measure of information is defined with Lyapunov vectors in tangent space, making it less akin to the classical Fisher information and more akin to the quantum Fisher information defined with wavevectors in Hilbert space. Our analysis of the local state space structure and linear stability leads to upper and lower bounds on this information, giving it an interpretation as the net stretching action of the flow. Numerical calculations of this information for illustrative mechanical examples show that it depends directly on the phase space curvature and speed of the flow.
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Affiliation(s)
- Mohamed Sahbani
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
- Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Swetamber Das
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
- Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
- Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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Mondal S, Greenberg JS, Green JR. Dynamic scaling of stochastic thermodynamic observables for chemical reactions at and away from equilibrium. J Chem Phys 2022; 157:194105. [DOI: 10.1063/5.0106714] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Physical kinetic roughening processes are well-known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the chemical reaction mechanisms available synthetically and occurring naturally? Here, we formulate an approach to the dynamic scaling of stochastic fluctuations in thermodynamic observables at and away from equilibrium. Both analytical expressions and numerical simulations confirm our dynamic scaling ansatz with associated scaling exponents, function, and law. A survey of common chemical mechanisms reveals classes that organize according to the molecularity of the reactions involved, the nature of the reaction vessel and external reservoirs, (non)equilibrium conditions, and the extent of autocatalysis in the reaction network. Varying experimental parameters, such as temperature, can cause coupled reactions capable of chemical feedback to transition between these classes. While path observables, such as the dynamical activity, have scaling exponents that are time-independent, the variance in the entropy production and flow can have time-dependent scaling exponents and self-averaging properties as a result of temporal correlations that emerge during thermodynamically irreversible processes. Altogether, these results establish dynamic universality classes in the nonequilibrium fluctuations of thermodynamic observables for well-mixed chemical reactions.
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Affiliation(s)
- Shrabani Mondal
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
- Department of Chemistry, Physical Chemistry Section, Jadavpur University, Kolkata 700032, India
| | - Jonah S. Greenberg
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
| | - Jason R. Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
- Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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Das S, Green JR. Density matrix formulation of dynamical systems. Phys Rev E 2022; 106:054135. [PMID: 36559452 DOI: 10.1103/physreve.106.054135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Accepted: 10/07/2022] [Indexed: 06/17/2023]
Abstract
Physical systems that are dissipating, mixing, and developing turbulence also irreversibly transport statistical density. However, predicting the evolution of density from atomic and molecular scale dynamics is challenging for nonsteady, open, and driven nonequilibrium processes. Here, we establish a theory to address this challenge for classical dynamical systems that is analogous to the density matrix formulation of quantum mechanics. We show that a classical density matrix is similar to the phase-space metric and evolves in time according to generalizations of Liouville's theorem and Liouville's equation for non-Hamiltonian systems. The traditional Liouvillian forms are recovered in the absence of dissipation or driving by imposing trace preservation or by considering Hamiltonian dynamics. Local measures of dynamical instability and chaos are embedded in classical commutators and anticommutators and directly related to Poisson brackets when the dynamics are Hamiltonian. Because the classical density matrix is built from the Lyapunov vectors that underlie classical chaos, it offers an alternative computationally tractable basis for the statistical mechanics of nonequilibrium processes that applies to systems that are driven, transient, dissipative, regular, and chaotic.
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Affiliation(s)
- Swetamber Das
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA and Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA and Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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Craven GT, Lubbers N, Barros K, Tretiak S. Ex Machina Determination of Structural Correlation Functions. J Phys Chem Lett 2020; 11:4372-4378. [PMID: 32370504 DOI: 10.1021/acs.jpclett.0c00627] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Determining the structural properties of condensed-phase systems is a fundamental problem in theoretical statistical mechanics. Here we present a machine learning method that is able to predict structural correlation functions with significantly improved accuracy in comparison with traditional approaches. The usefulness of this ex machina (from the machine) approach is illustrated by predicting the radial distribution functions of two paradigmatic condensed-phase systems, a Lennard-Jones fluid and a hard-sphere fluid, and then comparing those results to the results obtained using both integral equation methods and empirically motivated analytical functions. We find that application of the developed ex machina method typically decreases the predictive error by more than an order of magnitude in comparison with traditional theoretical methods.
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Affiliation(s)
- Galen T Craven
- Theoretical Division and Center for Nonlinear Studies (CNLS), Los Alamos National Laboratory, Los Alamos, New Mexico 87544, United States
| | - Nicholas Lubbers
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, United States
| | - Kipton Barros
- Theoretical Division and Center for Nonlinear Studies (CNLS), Los Alamos National Laboratory, Los Alamos, New Mexico 87544, United States
| | - Sergei Tretiak
- Theoretical Division, Center for Nonlinear Studies (CNLS), and Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, New Mexico 87544, United States
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Abstract
Fluids cooled to the liquid–vapor critical point develop system-spanning fluctuations in density that transform their visual appearance. Despite a rich phenomenology, however, there is not currently an explanation of the mechanical instability in the molecular motion at this critical point. Here, we couple techniques from nonlinear dynamics and statistical physics to analyze the emergence of this singular state. Numerical simulations and analytical models show how the ordering mechanisms of critical dynamics are measurable through the hierarchy of spatiotemporal Lyapunov vectors. A subset of unstable vectors soften near the critical point, with a marked suppression in their characteristic exponents that reflects a weakened sensitivity to initial conditions. Finite-time fluctuations in these exponents exhibit sharply peaked dynamical timescales and power law signatures of the critical dynamics. Collectively, these results are symptomatic of a critical slowing down of chaos that sits at the root of our statistical understanding of the liquid–vapor critical point. It is well known that fluids become opaque at the liquid–vapor critical point, but a description of the underlying mechanical instability is still missing. Das and Green leverage nonlinear dynamics to quantify the role of chaos in the emergence of this critical phenomenon.
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Stegehuis C, Hofstad RVD, van Leeuwaarden JSH. Variational principle for scale-free network motifs. Sci Rep 2019; 9:6762. [PMID: 31043621 PMCID: PMC6494877 DOI: 10.1038/s41598-019-43050-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2018] [Accepted: 04/15/2019] [Indexed: 11/30/2022] Open
Abstract
For scale-free networks with degrees following a power law with an exponent τ ∈ (2, 3), the structures of motifs (small subgraphs) are not yet well understood. We introduce a method designed to identify the dominant structure of any given motif as the solution of an optimization problem. The unique optimizer describes the degrees of the vertices that together span the most likely motif, resulting in explicit asymptotic formulas for the motif count and its fluctuations. We then classify all motifs into two categories: motifs with small and large fluctuations.
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Affiliation(s)
- Clara Stegehuis
- Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, Netherlands.
| | - Remco van der Hofstad
- Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, Netherlands
| | - Johan S H van Leeuwaarden
- Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, Netherlands
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