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Rose M, Manikandan SK. Role of interactions in nonequilibrium transformations. Phys Rev E 2024; 109:044136. [PMID: 38755940 DOI: 10.1103/physreve.109.044136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2023] [Accepted: 03/28/2024] [Indexed: 05/18/2024]
Abstract
For arbitrary nonequilibrium transformations in complex systems, we show that the distance between the current state and a target state can be decomposed into two terms: one corresponding to an independent estimate of the distance, and another corresponding to interactions, quantified using the relative mutual information between the variables. This decomposition is a special case of a more general decomposition involving successive orders of correlation or interactions among the degrees of freedom of the system. To illustrate its practical significance, we study the thermal relaxation of two interacting, optically trapped colloidal particles, where increasing pairwise interaction strength is shown to prolong the longevity of the time-dependent nonequilibrium state. Additionally, we study a system with both pairwise and triplet interactions, where our approach identifies their distinct contributions to the transformation. In more general setups where it is possible to control the strength of different orders of interactions, our findings provide a way to disentangle their effects and identify interactions that facilitate the transformation.
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Affiliation(s)
- Maria Rose
- School of Pure and Applied Physics, Mahatma Gandhi University, 686560 Kottayam, India
| | - Sreekanth K Manikandan
- NORDITA, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden and Department of Chemistry, Stanford University, Stanford, California 94305, USA
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2
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Tang Y, Liu J, Zhang J, Zhang P. Learning nonequilibrium statistical mechanics and dynamical phase transitions. Nat Commun 2024; 15:1117. [PMID: 38321012 PMCID: PMC10847122 DOI: 10.1038/s41467-024-45172-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 01/15/2024] [Indexed: 02/08/2024] Open
Abstract
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also poses new challenges as the distribution evolves over time. Characterizing dynamical phase transitions as an emergent behavior further requires tracking nonequilibrium systems under a control parameter. While a number of methods have been proposed, such as tensor networks for one-dimensional lattices, we lack a method for arbitrary time beyond the steady state and for higher dimensions. Here, we develop a general computational framework to study the time evolution of nonequilibrium systems in statistical mechanics by leveraging variational autoregressive networks, which offer an efficient computation on the dynamical partition function, a central quantity for discovering the phase transition. We apply the approach to prototype models of nonequilibrium statistical mechanics, including the kinetically constrained models of structural glasses up to three dimensions. The approach uncovers the active-inactive phase transition of spin flips, the dynamical phase diagram, as well as new scaling relations. The result highlights the potential of machine learning dynamical phase transitions in nonequilibrium systems.
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Affiliation(s)
- Ying Tang
- Institute of Fundamental and Frontier Sciences, University of Electronic Sciences and Technology of China, Chengdu, 611731, China.
- International Academic Center of Complex Systems, Beijing Normal University, Zhuhai, 519087, China.
| | - Jing Liu
- CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Systems Science, Beijing Normal University, Beijing, 100875, China
| | - Jiang Zhang
- School of Systems Science, Beijing Normal University, Beijing, 100875, China
- Swarma Research, Beijing, 102308, China
| | - Pan Zhang
- CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou, 310024, China.
- Hefei National Laboratory, Hefei, 230088, China.
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3
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Hack P, Gottwald S, Braun DA. Jarzyski's Equality and Crooks' Fluctuation Theorem for General Markov Chains with Application to Decision-Making Systems. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1731. [PMID: 36554136 PMCID: PMC9777588 DOI: 10.3390/e24121731] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Revised: 11/19/2022] [Accepted: 11/24/2022] [Indexed: 06/17/2023]
Abstract
We define common thermodynamic concepts purely within the framework of general Markov chains and derive Jarzynski's equality and Crooks' fluctuation theorem in this setup. In particular, we regard the discrete-time case, which leads to an asymmetry in the definition of work that appears in the usual formulation of Crooks' fluctuation theorem. We show how this asymmetry can be avoided with an additional condition regarding the energy protocol. The general formulation in terms of Markov chains allows transferring the results to other application areas outside of physics. Here, we discuss how this framework can be applied in the context of decision-making. This involves the definition of the relevant quantities, the assumptions that need to be made for the different fluctuation theorems to hold, as well as the consideration of discrete trajectories instead of the continuous trajectories, which are relevant in physics.
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Affiliation(s)
- Pedro Hack
- Institute of Neural Information Processing, Ulm University, 89081 Ulm, Germany
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Mamede IN, Harunari PE, Akasaki BAN, Proesmans K, Fiore CE. Obtaining efficient thermal engines from interacting Brownian particles under time-periodic drivings. Phys Rev E 2022; 105:024106. [PMID: 35291114 DOI: 10.1103/physreve.105.024106] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 01/18/2022] [Indexed: 06/14/2023]
Abstract
We introduce an alternative route for obtaining reliable cyclic engines, based on two interacting Brownian particles under time-periodic drivings which can be used as a work-to-work converter or a heat engine. Exact expressions for the thermodynamic fluxes, such as power and heat, are obtained using the framework of stochastic thermodynamic. We then use these exact expression to optimize the driving protocols with respect to output forces, their phase difference. For the work-to-work engine, they are solely expressed in terms of Onsager coefficients and their derivatives, whereas nonlinear effects start to play a role since the particles are at different temperatures. Our results suggest that stronger coupling generally leads to better performance, but careful design is needed to optimize the external forces.
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Affiliation(s)
- Iago N Mamede
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
| | - Pedro E Harunari
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Bruno A N Akasaki
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
| | - Karel Proesmans
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
- Hasselt University, B-3590 Diepenbeek, Belgium
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen, Denmark
| | - C E Fiore
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
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Akasaki BAN, de Oliveira MJ, Fiore CE. Entropy production and heat transport in harmonic chains under time-dependent periodic drivings. Phys Rev E 2020; 101:012132. [PMID: 32069596 DOI: 10.1103/physreve.101.012132] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2019] [Indexed: 11/07/2022]
Abstract
Using stochastic thermodynamics, the properties of interacting linear chains subject to periodic drivings are investigated. The systems are described by Fokker-Planck-Kramers equation and exact solutions are obtained as functions of the modulation frequency and strength constants. Analysis will be carried out for short and long chains. In the former case, explicit expressions are derived for a chain of two particles, in which the entropy production is written down as a bilinear function of thermodynamic forces and fluxes, whose associated Onsager coefficients are evaluated for distinct kinds of periodic drivings. The limit of long chains is analyzed by means of a protocol in which the intermediate temperatures are self-consistently chosen and the entropy production is decomposed as a sum of two individual contributions, one coming from real baths (placed at extremities of lattice) and other from self-consistent baths. Whenever the former dominates for short chains, the latter contribution prevails for long ones. The thermal reservoirs lead to a heat flux according to Fourier's law.
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Affiliation(s)
- Bruno A N Akasaki
- Universidade de São Paulo, Instituto de Física, Rua do Matão, 1371, 05508-090 São Paulo, SP, Brazil
| | - Mário J de Oliveira
- Universidade de São Paulo, Instituto de Física, Rua do Matão, 1371, 05508-090 São Paulo, SP, Brazil
| | - C E Fiore
- Universidade de São Paulo, Instituto de Física, Rua do Matão, 1371, 05508-090 São Paulo, SP, Brazil
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Tang Y, Xu S, Ao P. Escape rate for nonequilibrium processes dominated by strong non-detailed balance force. J Chem Phys 2018; 148:064102. [PMID: 29448766 DOI: 10.1063/1.5008524] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantifying the escape rate from a meta-stable state is essential to understand a wide range of dynamical processes. Kramers' classical rate formula is the product of an exponential function of the potential barrier height and a pre-factor related to the friction coefficient. Although many applications of the rate formula focused on the exponential term, the prefactor can have a significant effect on the escape rate in certain parameter regions, such as the overdamped limit and the underdamped limit. There have been continuous interests to understand the effect of non-detailed balance on the escape rate; however, how the prefactor behaves under strong non-detailed balance force remains elusive. In this work, we find that the escape rate formula has a vanishing prefactor with decreasing friction strength under the strong non-detailed balance limit. We both obtain analytical solutions in specific examples and provide a derivation for more general cases. We further verify the result by simulations and propose a testable experimental system of a charged Brownian particle in electromagnetic field. Our study demonstrates that a special care is required to estimate the effect of prefactor on the escape rate when non-detailed balance force dominates.
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Affiliation(s)
- Ying Tang
- Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Song Xu
- Department of Biomathematics, University of California at Los Angeles, Los Angeles, California 90095-1766, USA
| | - Ping Ao
- Key Laboratory of Systems Biomedicine Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China
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Wang G, Yuan R, Zhu X, Ao P. Endogenous Molecular-Cellular Network Cancer Theory: A Systems Biology Approach. Methods Mol Biol 2018; 1702:215-245. [PMID: 29119508 DOI: 10.1007/978-1-4939-7456-6_11] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
In light of ever apparent limitation of the current dominant cancer mutation theory, a quantitative hypothesis for cancer genesis and progression, endogenous molecular-cellular network hypothesis has been proposed from the systems biology perspective, now for more than 10 years. It was intended to include both the genetic and epigenetic causes to understand cancer. Its development enters the stage of meaningful interaction with experimental and clinical data and the limitation of the traditional cancer mutation theory becomes more evident. Under this endogenous network hypothesis, we established a core working network of hepatocellular carcinoma (HCC) according to the hypothesis and quantified the working network by a nonlinear dynamical system. We showed that the two stable states of the working network reproduce the main known features of normal liver and HCC at both the modular and molecular levels. Using endogenous network hypothesis and validated working network, we explored genetic mutation pattern in cancer and potential strategies to cure or relieve HCC from a totally new perspective. Patterns of genetic mutations have been traditionally analyzed by posteriori statistical association approaches in light of traditional cancer mutation theory. One may wonder the possibility of a priori determination of any mutation regularity. Here, we found that based on the endogenous network theory the features of genetic mutations in cancers may be predicted without any prior knowledge of mutation propensities. Normal hepatocyte and cancerous hepatocyte stable states, specified by distinct patterns of expressions or activities of proteins in the network, provide means to directly identify a set of most probable genetic mutations and their effects in HCC. As the key proteins and main interactions in the network are conserved through cell types in an organism, similar mutational features may also be found in other cancers. This analysis yielded straightforward and testable predictions on an accumulated and preferred mutation spectrum in normal tissue. The validation of predicted cancer state mutation patterns demonstrates the usefulness and potential of a causal dynamical framework to understand and predict genetic mutations in cancer. We also obtained the following implication related to HCC therapy, (1) specific positive feedback loops are responsible for the maintenance of normal liver and HCC; (2) inhibiting proliferation and inflammation-related positive feedback loops, and simultaneously inducing liver-specific positive feedback loop is predicated as the potential strategy to cure or relieve HCC; (3) the genesis and regression of HCC is asymmetric. In light of the characteristic property of the nonlinear dynamical system, we demonstrate that positive feedback loops must be existed as a simple and general molecular basis for the maintenance of phenotypes such as normal liver and HCC, and regulating the positive feedback loops directly or indirectly provides potential strategies to cure or relieve HCC.
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Affiliation(s)
- Gaowei Wang
- Ministry of Education Key Laboratory of Systems Biomedicine, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai, China
- Department of Pathology, University of California, San Diego, La Jolla, CA, 92093-0864, USA
| | - Ruoshi Yuan
- Ministry of Education Key Laboratory of Systems Biomedicine, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai, China
- Department of Systems Biology, Harvard University, Boston, MA, USA
| | - Xiaomei Zhu
- Ministry of Education Key Laboratory of Systems Biomedicine, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai, China
- Shanghai Center for Quantitative Life Sciences and Physics Department, Shanghai University, Shanghai, China
| | - Ping Ao
- Ministry of Education Key Laboratory of Systems Biomedicine, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai, China.
- Shanghai Center for Quantitative Life Sciences and Physics Department, Shanghai University, Shanghai, China.
- State Key Laboratory for Oncogenes and Related Genes, Shanghai Cancer Institute, Shanghai Jiao Tong University School of Medicine, Shanghai, China.
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Potential landscape of high dimensional nonlinear stochastic dynamics with large noise. Sci Rep 2017; 7:15762. [PMID: 29150680 PMCID: PMC5693902 DOI: 10.1038/s41598-017-15889-2] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2017] [Accepted: 10/02/2017] [Indexed: 12/14/2022] Open
Abstract
Quantifying stochastic processes is essential to understand many natural phenomena, particularly in biology, including the cell-fate decision in developmental processes as well as the genesis and progression of cancers. While various attempts have been made to construct potential landscape in high dimensional systems and to estimate transition rates, they are practically limited to the cases where either noise is small or detailed balance condition holds. A general and practical approach to investigate real-world nonequilibrium systems, which are typically high-dimensional and subject to large multiplicative noise and the breakdown of detailed balance, remains elusive. Here, we formulate a computational framework that can directly compute the relative probabilities between locally stable states of such systems based on a least action method, without the necessity of simulating the steady-state distribution. The method can be applied to systems with arbitrary noise intensities through A-type stochastic integration, which preserves the dynamical structure of the deterministic counterpart dynamics. We demonstrate our approach in a numerically accurate manner through solvable examples. We further apply the method to investigate the role of noise on tumor heterogeneity in a 38-dimensional network model for prostate cancer, and provide a new strategy on controlling cell populations by manipulating noise strength.
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Mandal D, DeWeese MR. Nonequilibrium work energy relation for non-Hamiltonian dynamics. Phys Rev E 2016; 93:042129. [PMID: 27176276 DOI: 10.1103/physreve.93.042129] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2015] [Indexed: 06/05/2023]
Abstract
Recent years have witnessed major advances in our understanding of nonequilibrium processes. The Jarzynski equality, for example, provides a link between equilibrium free energy differences and finite-time nonequilibrium dynamics. We propose a generalization of this relation to non-Hamiltonian dynamics, relevant for active matter systems, continuous feedback, and computer simulation. Surprisingly, this relation allows us to calculate the free energy difference between the desired initial and final equilibrium states using arbitrary dynamics. As a practical matter, this dissociation between the dynamics and the initial and final states promises to facilitate a range of techniques for free energy estimation in a single universal expression.
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Affiliation(s)
- Dibyendu Mandal
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Michael R DeWeese
- Department of Physics, University of California, Berkeley, California 94720, USA
- Redwood Center for Theoretical Neuroscience and Helen Wills Neuroscience Institute, University of California, Berkeley, California 94720, USA
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Tang Y, Yuan R, Ao P. Anomalous free energy changes induced by topology. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062129. [PMID: 26764654 DOI: 10.1103/physreve.92.062129] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2015] [Indexed: 06/05/2023]
Abstract
We report that nontrivial topology of a driven Brownian particle restricted on a ring leads to anomalous behaviors on free energy change. Starting from steady states with identical distribution and current on the ring, free energy changes are distinct and nonperiodic after the system is driven by the same periodic force protocol. We demonstrate our observation in examples through both exact solutions and numerical simulations. The free energy calculated here can be measured in recent experimental systems.
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Affiliation(s)
- Ying Tang
- Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Key Laboratory of Systems Biomedicine Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ruoshi Yuan
- School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ping Ao
- Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Key Laboratory of Systems Biomedicine Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China
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