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Yutaka Nakada - One of the best experts on this subject based on the ideXlab platform.
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Temporal extensivity of Tsallis' Entropy and the bound on Entropy Production Rate.
Physical review. E Statistical nonlinear and soft matter physics, 2006Co-Authors: Sumiyoshi Abe, Yutaka NakadaAbstract:The Tsallis Entropy, which is a generalization of the Boltzmann-Gibbs Entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation for the Tsallis Entropy. They are primarily concerned with nonlinear dynamical systems at the edge of chaos. Here, it is shown by generalizing a formulation of thermostatistics based on time averages recently proposed by Carati [A. Carati, Physica A 348, 110 (2005)] that, whenever relevant, the Tsallis Entropy indexed by q is temporally extensive: linear growth in time, i.e., finite Entropy Production Rate. Then, the universal bound on the Entropy Production Rate is shown to be 1/ absolute value (1-q). The property of the associated probabilistic process, i.e., the sojourn time distribution, determining randomness of motion in phase space is also analyzed.
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Temporal extensivity of Tsallis' Entropy and the bound on Entropy Production Rate.
Physical Review E, 2006Co-Authors: Sumiyoshi Abe, Yutaka NakadaAbstract:The Tsallis Entropy, which is a generalization of the Boltzmann-Gibbs Entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation for the Tsallis Entropy. They are primarily concerned with nonlinear dynamical systems at the edge of chaos. Here, it is shown by generalizing a formulation of thermostatistics based on time averages recently proposed by Carati [A. Carati, Physica A 348, 110 (2005)] that, whenever relevant, the Tsallis Entropy indexed by $q$ is temporally extensive: linear growth in time, i.e., finite Entropy Production Rate. Then, the universal bound on the Entropy Production Rate is shown to be $1/|1-q|$ . The property of the associated probabilistic process, i.e., the sojourn time distribution, determining randomness of motion in phase space is also analyzed.Comment: 25 pages, no figure
Tatsuaki Tsuruyama - One of the best experts on this subject based on the ideXlab platform.
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Non-equilibrium thermodynamics of biological signal transduction predicts conservation of Entropy Production Rate.
Journal of theoretical biology, 2019Co-Authors: Tatsuaki TsuruyamaAbstract:Abstract Studies have reported that bio-cellular signal transduction can be investigated based on thermodynamics. This short article aims to consider signal transduction carried out by signaling molecules from the perspective of non-equilibrium thermodynamics. Under conditions in which total Entropy Production Rate was minimized, the Entropy Production Rate per signaling molecule was conserved independently of the steps during signal transduction. Accordingly, the conserved Production Rate can be defined as the channel capacity of the given signal transduction cascade. Non- equilibrium thermodynamics provides a theoretical framework for cell signal transduction.
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An information thermodynamic approach quantifying MAPK-related signaling cascades by average Entropy Production Rate
2018Co-Authors: Tatsuaki TsuruyamaAbstract:Information thermodynamics has recently greatly developed the application for analysis of biological phenomenon. During the signal transduction, Entropy Production from phosphorylation of signal molecule is produced at individual step Production. Using this value, average Entropy Production Rate (AEPR) is computable. In the current study, AEPR in each signal step was analyzed using experimental data from previously reported studies of the mitogen-activated protein kinases (MAPK) cascade. The result revealed that the differences of AEPR is smaller when using ligands, suggesting that AEPR is one of the attributes of the given cascade and useful for quantitative analysis. This consistency of AEPR suggests that the number of signal events is maximized, in other words, signaling efficiency is maximized. In conclusion, the current information theoretical approach provides not only a quantitative means for comparison of responses to a specified extracellular stimulation, but also a method for evaluation of active cascades.
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The Conservation of Average Entropy Production Rate in a Model of Signal Transduction: Information Thermodynamics Based on the Fluctuation Theorem.
Entropy (Basel Switzerland), 2018Co-Authors: Tatsuaki TsuruyamaAbstract:Cell signal transduction is a non-equilibrium process characterized by the reaction cascade. This study aims to quantify and compare signal transduction cascades using a model of signal transduction. The signal duration was found to be linked to step-by-step transition probability, which was determined using information theory. By applying the fluctuation theorem for reversible signal steps, the transition probability was described using the average Entropy Production Rate. Specifically, when the signal event number during the cascade was maximized, the average Entropy Production Rate was found to be conserved during the entire cascade. This approach provides a quantitative means of analyzing signal transduction and identifies an effective cascade for a signaling network.
Z. Kovacs - One of the best experts on this subject based on the ideXlab platform.
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Fluctuation formula in the Nosé-Hoover thermostated Lorentz gas.
Physical Review E, 2005Co-Authors: M. Dolowschiak, Z. KovacsAbstract:In this paper we examine numerically the Gallavotti-Cohen fluctuation formula for phase-space contraction Rate and Entropy Production Rate fluctuations in the Nos\'e-Hoover thermostated periodic Lorentz gas. Our results indicate that while the phase-space contraction Rate fluctuations violate the fluctuation formula near equilibrium states, the Entropy Production Rate fluctuations obey this formula near and far from equilibrium states as well.
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Fluctuation formula in the Nosé-Hoover thermostated Lorentz gas.
Physical review. E Statistical nonlinear and soft matter physics, 2005Co-Authors: M. Dolowschiak, Z. KovacsAbstract:In this paper we examine numerically the Gallavotti-Cohen fluctuation formula for phase-space contraction Rate and Entropy Production Rate fluctuations in the Nosé-Hoover thermostated periodic Lorentz gas. Our results indicate that while the phase-space contraction Rate fluctuations violate the fluctuation formula near equilibrium states, the Entropy Production Rate fluctuations obey this formula near and far from equilibrium states as well.
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Fluctuation formula and non-Gaussian distribution of the Entropy Production Rate in the thermostated Lorentz gas
arXiv: Chaotic Dynamics, 2002Co-Authors: M. Dolowschiak, Z. KovacsAbstract:In this paper we numerically examine the connection of the Gallavotti-Cohen fluctuation formula and the functional form of the corresponding probability density function in the field driven Lorentz gas thermostated by the Gaussian isokinetic thermostat. We analyze the moments of the Entropy Production Rate fluctuations and show that all the central moments of the averaged fluctuations exhibit power law dependence on the length of the averaging time interval, indicating that this density deviates from a Gaussian. Furthermore the obtained exponents are found to obey a special pairing rule showing that the corresponding probability density function can not be scaled in the averaging time interval.
Jainagesh A Sekhar - One of the best experts on this subject based on the ideXlab platform.
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Solidification Morphology and Bifurcation Predictions with the Maximum Entropy Production Rate Model.
Entropy (Basel Switzerland), 2019Co-Authors: Yaw Delali Bensah, Jainagesh A SekharAbstract:The use of the principle of maximum Entropy generation per unit volume is a new approach in materials science that has implications for understanding the morphological evolution during solid-liquid interface growth, including bifurcations with or without diffuseness. A review based on a pre-publication arXiv preprint is first presented. A detailed comparison with experimental observations indicates that the Maximum Entropy Production Rate-density model (MEPR) can correctly predict bifurcations for dilute alloys during solidification. The model predicts a critical diffuseness of the interface at which a plane-front or any other form of diffuse interface will become unstable. A further confidence test for the model is offered in this article by comparing the predicted liquid diffusion coefficients to those obtained experimentally. A comparison of the experimentally determined solute diffusion constant in dilute binary Pb-Sn alloys with those predicted by the various solidification instability models (1953-2011) is additionally discussed. A good predictability is noted for the MEPR model when the interface diffuseness is small. In comparison, the more traditional interface break-down models have low predictiveness.
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morphological assessment with the maximum Entropy Production Rate mepr postulate
Current opinion in chemical engineering, 2014Co-Authors: Yaw Delali Bensah, Jainagesh A SekharAbstract:The three established techniques that are currently employed for the prediction of solidification bifurcations and the shape of cast microstructures are reviewed. The main limitations of these established techniques are discussed with examples. A more recent model called the maximum Entropy Production Rate (MEPR) postulate is also reviewed as to its ability to predict patterns, especially those that form during positive temperature gradient solidification. The principle of MEPR states that if there are sufficient degrees of freedom within a system, it will adopt a stable state at which the Entropy generation Rate is maximized in an open thermodynamic system. In the context of steady state solidification, pathway selections are reflected in the overall steady-state morphological features and shape-bifurcations that are noted with a change in the Rate of solidification.
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The description of morphologically stable regimes for steady state solidification based on the maximum Entropy Production Rate postulate
Journal of Materials Science, 2011Co-Authors: Jainagesh A SekharAbstract:The maximum Entropy Production Rate (MEPR) in the solid–liquid zone is developed and tested as a possible postulate for predicting the stable morphology for the special case of steady state directional solidification (DS). The principle of MEPR states that, if there are sufficient degrees of freedom within a system, it will adopt a stable state at which the Entropy generation (Production) Rate is maximized. Where feasible, the system will also try and adopt a steady state. The MEPR postulate determines the most probable state and therefore allows pathway selections to occur in an open thermodynamic system. In the context of steady state solidification, pathway selections are reflected in the corresponding morphological selections made by the system in the solid–liquid (mushy) zone in order to cope with the required Entropy Production. Steady state solidification is feasible at both close to, and far from equilibrium conditions. Based on MEPR, a model is proposed for examining the stability of various morphologies that have been experimentally observed during steady state directional solidification. This model employs a control volume approach for Entropy balance, including the Entropy generation term ( S _gen), which depends on the diffuse zone and average temperature of the solid–liquid region within the control volume. In this manner, the model takes a different approach from the successful kinetic models that have been able to predict key features of stable morphological patterns. Unstable planar interfaces, faceted cellular arrays, cell–dendrite transitions, half cells both faceted and smooth, and other transitions such as the absolute stability transition at high solid/liquid velocities are examined with the model. Uncommon solidification morphological features such as non - crystallographic dendrites and discontinuous cell-tip splitting are also examined with the model. The preferred morphological change-direction for the emergence of the stable morphological feature is inferred with the MEPR postulate in a manner analogous to the free energy minimization principle(s) when used for predicting phase stability and metastable phase formation. Aspects of mixed-mode order transformation characteristics are also discussed for non-equilibrium solidification containing a diffuse interface, in contrast to classifying solidification as purely a first order transformation. The MEPR model predictions are shown to follow the experimental transitions observed to date in several historical studies.
Jie Xiong - One of the best experts on this subject based on the ideXlab platform.
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the large deviation principle and steady state fluctuation theorem for the Entropy Production Rate of a stochastic process in magnetic fields
Journal of Mathematical Physics, 2016Co-Authors: Yong Chen, Jie XiongAbstract:Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. There exist very few results for steady-state fluctuation theorem of sample Entropy Production Rate in terms of large deviation principle for diffusion processes due to the technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and Rate function. The proof is based on the Karhunen-Loeve expansion of complex-valued Ornstein-Uhlenbeck process.
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Asymptotics of Sample Entropy Production Rate for Stochastic Differential Equations
Journal of Statistical Physics, 2016Co-Authors: Feng-yu Wang, Jie XiongAbstract:Using the dimension-free Harnack inequality and the integration by parts formula for the associated diffusion semigroup, we prove the central limit theorem, the modeRate deviation principle, and the logarithmic iteration law for the sample Entropy Production Rate of a family of stochastic differential equations.
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The large deviation principle and steady-state fluctuation theorem for the Entropy Production Rate of a stochastic process in magnetic fields
Journal of Mathematical Physics, 2016Co-Authors: Yong Chen, Jie XiongAbstract:Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. Steady-state fluctuation theorem of sample Entropy Production Rate in terms of large deviation principle for diffusion processes have not been rigorously proved yet due to technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and Rate function. The proof is based on the Karhunen-Lo\'{e}ve expansion of complex-valued Ornstein-Uhlenbeck process
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asymptotics of sample Entropy Production Rate for stochastic differential equations
arXiv: Probability, 2015Co-Authors: Feng-yu Wang, Jie XiongAbstract:By using the dimension-free Harnack inequality and the integration by parts formula for the associated diffusion semigroup, we prove the central limit theorem, the modeRate deviation principle, and the logarithmic iteration law for the sample Entropy Production Rate of stochastic differential equations with Lipschitz continuous and dissipative drifts.