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Gian Paolo Beretta - One of the best experts on this subject based on the ideXlab platform.
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QUANTUM THERMODYNAMICS: MICROSCOPIC FOUNDATIONS OF ENTROPY AND OF ENTROPY GENERATION BY IRREVERSIBILITY
2015Co-Authors: Gian Paolo BerettaAbstract:ABSTRACT. What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? Most physicists still accept and teach that the rationalization of these fundamental ques-tions is given by Statistical Mechanics. Indeed, for everyday laboratory physics, the math-ematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the ther-modynamic equilibrium properties of matter, including entropy values. However, as al-ready recognized by Schrödinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibilit
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NONLINEAR DYNAMICAL EQUATION FOR IRREVERSIBLE, STEEPEST-ENTROPY-ASCENT RELAXATION TO STABLE EQUILIBRIUM
2015Co-Authors: Gian Paolo BerettaAbstract:Abstract. We discuss the structure and main features of the nonlinear evolution equation proposed by this author as the fundamental dynamical law within the framework of Quantum Thermodynamics. The nonlinear equation generates a dynam-ical group providing a unique deterministic description of irreversible, conservative relaxation towards equilibrium from any non-equilibrium state, and satisfies a very restrictive stability requirement equivalent to Hatsopoulos-Keenan statement of the second law of thermodynamics. Here, we emphasize its mathematical structure and its applicability also within other contexts
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Nonlinear quantum evolution equations to model irreversible adiabatic relaxation with maximal entropy production and other nonunitary processes
2013Co-Authors: Gian Paolo BerettaAbstract:We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropyascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum theory of irreversibility and thermodynamics for a single isolated or adiabatic particle, qubit, or qudit, and recently rediscovered by other authors. The nonlinear equation generates a dynamical group, not just a semigroup, providing a deterministic description of irreversible conservative relaxation towards equilibrium from any non-equilibrium density operator. It satisfies a very restrictive stability requirement equivalent to the Hatsopoulos-Keenan statement of the second law of thermodynamics. We then examine the form of the evolution equation we proposed to describe multipartite isolated or adiabatic systems. This hinges on novel nonlinear projections defining local operators that we interpret as “local perceptions ” of the overall system’s energy and entropy. Each component particle contributes an independent local tendency along the direction of steepest increase of the locally perceived entropy at constant locally perceived energy. It conserves both the locallyperceived energies and the overall energy, and meets strong separability and non-signaling conditions, even though the local evolutions are not independent of existing correlations. We finally show how the geometrical construction can readily lead to other thermodynamically relevant models, such as of the nonunitary isoentropic evolution needed for full extraction of a system’s adiabatic availability
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nonlinear quantum evolution equations to model irreversible adiabatic relaxation with maximal entropy production and other nonunitary processes
Reports on Mathematical Physics, 2009Co-Authors: Gian Paolo BerettaAbstract:We first discuss the geometrical construction and the main mathematical features of the maximum-entropy production/steepest-entropy-ascent nonlinear evolution equation proposed long time ago by this author in the framework of a fully quantum theory of irreversibility and ther modynamics for a single isolated or adiabatic particle, qubit, or qudit, and recently rediscovered by other authors. The nonlinear equation generates a dynamical group, not just a semigroup, providing a deterministic description of irreversible conservative relaxation towards equilibrium from any nonequilibrium density operator. It satisfies a very restrictive stability requirement equivalent to the Hatsopoulos-Keenan statement of the second law of thermodynamics. We then examine the form of the evolution equation we proposed to describe multipartite isolated or adiabatic systems. This hinges on novel nonlinear projections defining local operators that we interpret as "local perceptions" of the overall system's energy and entropy. Each component particle contributes an independent local tendency along the direction of steepest increase of the locally perceived entropy at constant locally perceived energy. It conserves both the locally perceived energies and the overall energy, and meets strong separability and nonsignaling con ditions, even though the local evolutions are not independent of existing correlations. We finally show how the geometrical construction can readily lead to other thermodynamically relevant models, such as of the nonunitary isoentropic evolution needed for full extraction of a system's adiabatic availability.
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Quantum thermodynamics: Microscopic foundations of entropy and of entropy generation by irreversibility
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche Matematiche e Naturali, 2008Co-Authors: Gian Paolo BerettaAbstract:What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? Most physicists still accept and teach that the rationalization of these fundamental questions is given by Statistical Mechanics. Indeed, for everyday laboratory physics, the mathematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. However, as already recognized by Schrodinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibility into the laws of microscopic physics. The result is a theory, that we call Quantum Thermodynamics, that has all the necessary features to combine Mechanics and Thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of Statistical Mechanics and the paradoxes on irreversibility, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity (therefore including chaotic behavior) and maximal-entropy-generation nonequilibrium dynamics. In this paper we discuss the background and formalism of Quantum Thermodynamics including its nonlinear equation of motion and the main general results. Our objective is to show in a not-too-technical manner that this theory provides indeed a complete and coherent resolution of the century-old dilemma on the meaning of entropy and the origin of irreversibility, including Onsager reciprocity relations and maximal-entropy-generation nonequilibrium dynamics, which we believe provides the microscopic foundations of heat, mass and momentum transfer theories, including all their implications such as Bejan's Constructal Theory of natural phenomena.
Robert Dyer - One of the best experts on this subject based on the ideXlab platform.
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Effects of Structure Variation on Solution Properties of Hydrotropes: Phenyl versus Cyclohexyl Chain Tips
2016Co-Authors: Marios Hopkins Hatzopoulos, Julian Eastoe, Peter J Dowding, Isabelle Grillo, Bruno Demé, Sarah E. Rogers, Richard Heenan, Robert DyerAbstract:The physicochemical behavior of the phenyl-n-alkanoate (PhenCx) and cyclohexyl-n-alkanoate (CyclohexCx) series has been investigated, supporting previous work on the understanding of hydrotropes (Hopkins Hatzopoulos, M.; Eastoe, J.; Dowding, P.J.; Rogers, S. E.; Heenan, R.; Dyer, R. Langmuir 2011, 27, 12346–12353). Electrical conductivity, surface tension, 1H NMR, and small-angle neutron scattering (SANS) were used to study adsorption and aggregation in terms of critical aggregation concentration (cac). The PhenCx series exhibited very similar d log(cac)/dn to n-alkylbenzoates (CnBenz), exhibiting two branches of behavior, with a common inflection point at four linear carbons, whereas the CyclohexCx series showed no break point. Electrical conductivity and 1H NMR concentration scans indicate a difference in physicochemical behavior between higher and lower homologues in both the PhenCx and CyclohexCx series. Surface tension measurements with compounds belonging to either group gave typical Gibbs adsorption profiles, having d log(cac)/dn curves consistent with limiting headgroup areas in the region of (35–55 Å2) indicating monolayer formation. SANS profiles showed no evidence for aggregates below the electrical conductivity determined cac values, inferring an “on–off” mode of aggregation. Analyses of SANS profiles was consistent with charged ellipsoidal aggregates, persisting from lower through to higher homologues in both the PhenCx and CyclohexCx series
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effects of structure variation on solution properties of hydrotropes phenyl versus cyclohexyl chain tips
Langmuir, 2012Co-Authors: Marios Hopkins Hatzopoulos, Julian Eastoe, Peter J Dowding, Isabelle Grillo, Bruno Deme, Sarah E Rogers, Richard K Heenan, Robert DyerAbstract:The physicochemical behavior of the phenyl-n-alkanoate (PhenCx) and cyclohexyl-n-alkanoate (CyclohexCx) series has been investigated, supporting previous work on the understanding of hydrotropes (Hopkins Hatzopoulos, M.; Eastoe, J.; Dowding, P.J.; Rogers, S. E.; Heenan, R.; Dyer, R. Langmuir2011, 27, 12346–12353). Electrical conductivity, surface tension, 1H NMR, and small-angle neutron scattering (SANS) were used to study adsorption and aggregation in terms of critical aggregation concentration (cac). The PhenCx series exhibited very similar d log(cac)/dn to n-alkylbenzoates (CnBenz), exhibiting two branches of behavior, with a common inflection point at four linear carbons, whereas the CyclohexCx series showed no break point. Electrical conductivity and 1H NMR concentration scans indicate a difference in physicochemical behavior between higher and lower homologues in both the PhenCx and CyclohexCx series. Surface tension measurements with compounds belonging to either group gave typical Gibbs adsorption...
Beretta, Gian Paolo - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear Quantum Evolution Equations to Model Irreversible Adiabatic Relaxation with Maximal Entropy Production and Other Nonunitary Processes
'Elsevier BV', 2009Co-Authors: Beretta, Gian PaoloAbstract:We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum theory of irreversibility and thermodynamics for a single isolated or adiabatic particle, qubit, or qudit, and recently rediscovered by other authors. The nonlinear equation generates a dynamical group, not just a semigroup, providing a deterministic description of irreversible conservative relaxation towards equilibrium from any non-equilibrium density operator. It satisfies a very restrictive stability requirement equivalent to the Hatsopoulos-Keenan statement of the second law of thermodynamics. We then examine the form of the evolution equation we proposed to describe multipartite isolated or adiabatic systems. This hinges on novel nonlinear projections defining local operators that we interpret as ``local perceptions'' of the overall system's energy and entropy. Each component particle contributes an independent local tendency along the direction of steepest increase of the locally perceived entropy at constant locally perceived energy. It conserves both the locally-perceived energies and the overall energy, and meets strong separability and non-signaling conditions, even though the local evolutions are not independent of existing correlations. We finally show how the geometrical construction can readily lead to other thermodynamically relevant models, such as of the nonunitary isoentropic evolution needed for full extraction of a system's adiabatic availability.Comment: To appear in Reports on Mathematical Physics. Presented at the The Jubilee 40th Symposium on Mathematical Physics, "Geometry & Quanta", Torun, Poland, June 25-28, 200
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Nonlinear Dynamical Equation for Irreversible, Steepest-Entropy-Ascent Relaxation to Stable Equilibrium
'AIP Publishing', 2007Co-Authors: Beretta, Gian PaoloAbstract:We discuss the structure and main features of the nonlinear evolution equation proposed by this author as the fundamental dynamical law within the framework of Quantum Thermodynamics. The nonlinear equation generates a dynamical group providing a unique deterministic description of irreversible, conservative relaxation towards equilibrium from any non-equilibrium state, and satisfies a very restrictive stability requirement equivalent to Hatsopoulos-Keenan statement of the second law of thermodynamics. Here, we emphasize its mathematical structure and its applicability also within other contexts, such as Classical and Quantum Statistical Mechanics, and Information Theory.Comment: Proceedings of the Conference "Quantum Theory: Reconsideration of Foundations - 4", Vaxjo, Sweden, June 11-16, 200
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The Hatsopoulos-Gyftopoulos resolution of the Schroedinger-Park paradox about the concept of "state" in quantum statistical mechanics
'World Scientific Pub Co Pte Lt', 2006Co-Authors: Beretta, Gian PaoloAbstract:A seldom recognized fundamental difficulty undermines the concept of individual ``state'' in the present formulations of quantum statistical mechanics (and in its quantum information theory interpretation as well). The difficulty is an unavoidable consequence of an almost forgotten corollary proved by E. Schroedinger in 1936 and perused by J.L. Park, Am. J. Phys., Vol. 36, 211 (1968). To resolve it, we must either reject as unsound the concept of state, or else undertake a serious reformulation of quantum theory and the role of statistics. We restate the difficulty and discuss a possible resolution proposed in 1976 by G.N. Hatsopoulos and E.P. Gyftopoulos, Found. Phys., Vol. 6, 15, 127, 439, 561 (1976).Comment: RevTeX4, 7 pages, corrected a paragraph and added an example at page 3, to appear in Mod. Phys. Lett.
Marios Hopkins Hatzopoulos - One of the best experts on this subject based on the ideXlab platform.
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Effects of Structure Variation on Solution Properties of Hydrotropes: Phenyl versus Cyclohexyl Chain Tips
2016Co-Authors: Marios Hopkins Hatzopoulos, Julian Eastoe, Peter J Dowding, Isabelle Grillo, Bruno Demé, Sarah E. Rogers, Richard Heenan, Robert DyerAbstract:The physicochemical behavior of the phenyl-n-alkanoate (PhenCx) and cyclohexyl-n-alkanoate (CyclohexCx) series has been investigated, supporting previous work on the understanding of hydrotropes (Hopkins Hatzopoulos, M.; Eastoe, J.; Dowding, P.J.; Rogers, S. E.; Heenan, R.; Dyer, R. Langmuir 2011, 27, 12346–12353). Electrical conductivity, surface tension, 1H NMR, and small-angle neutron scattering (SANS) were used to study adsorption and aggregation in terms of critical aggregation concentration (cac). The PhenCx series exhibited very similar d log(cac)/dn to n-alkylbenzoates (CnBenz), exhibiting two branches of behavior, with a common inflection point at four linear carbons, whereas the CyclohexCx series showed no break point. Electrical conductivity and 1H NMR concentration scans indicate a difference in physicochemical behavior between higher and lower homologues in both the PhenCx and CyclohexCx series. Surface tension measurements with compounds belonging to either group gave typical Gibbs adsorption profiles, having d log(cac)/dn curves consistent with limiting headgroup areas in the region of (35–55 Å2) indicating monolayer formation. SANS profiles showed no evidence for aggregates below the electrical conductivity determined cac values, inferring an “on–off” mode of aggregation. Analyses of SANS profiles was consistent with charged ellipsoidal aggregates, persisting from lower through to higher homologues in both the PhenCx and CyclohexCx series
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effects of structure variation on solution properties of hydrotropes phenyl versus cyclohexyl chain tips
Langmuir, 2012Co-Authors: Marios Hopkins Hatzopoulos, Julian Eastoe, Peter J Dowding, Isabelle Grillo, Bruno Deme, Sarah E Rogers, Richard K Heenan, Robert DyerAbstract:The physicochemical behavior of the phenyl-n-alkanoate (PhenCx) and cyclohexyl-n-alkanoate (CyclohexCx) series has been investigated, supporting previous work on the understanding of hydrotropes (Hopkins Hatzopoulos, M.; Eastoe, J.; Dowding, P.J.; Rogers, S. E.; Heenan, R.; Dyer, R. Langmuir2011, 27, 12346–12353). Electrical conductivity, surface tension, 1H NMR, and small-angle neutron scattering (SANS) were used to study adsorption and aggregation in terms of critical aggregation concentration (cac). The PhenCx series exhibited very similar d log(cac)/dn to n-alkylbenzoates (CnBenz), exhibiting two branches of behavior, with a common inflection point at four linear carbons, whereas the CyclohexCx series showed no break point. Electrical conductivity and 1H NMR concentration scans indicate a difference in physicochemical behavior between higher and lower homologues in both the PhenCx and CyclohexCx series. Surface tension measurements with compounds belonging to either group gave typical Gibbs adsorption...
Isabelle Grillo - One of the best experts on this subject based on the ideXlab platform.
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Effects of Structure Variation on Solution Properties of Hydrotropes: Phenyl versus Cyclohexyl Chain Tips
2016Co-Authors: Marios Hopkins Hatzopoulos, Julian Eastoe, Peter J Dowding, Isabelle Grillo, Bruno Demé, Sarah E. Rogers, Richard Heenan, Robert DyerAbstract:The physicochemical behavior of the phenyl-n-alkanoate (PhenCx) and cyclohexyl-n-alkanoate (CyclohexCx) series has been investigated, supporting previous work on the understanding of hydrotropes (Hopkins Hatzopoulos, M.; Eastoe, J.; Dowding, P.J.; Rogers, S. E.; Heenan, R.; Dyer, R. Langmuir 2011, 27, 12346–12353). Electrical conductivity, surface tension, 1H NMR, and small-angle neutron scattering (SANS) were used to study adsorption and aggregation in terms of critical aggregation concentration (cac). The PhenCx series exhibited very similar d log(cac)/dn to n-alkylbenzoates (CnBenz), exhibiting two branches of behavior, with a common inflection point at four linear carbons, whereas the CyclohexCx series showed no break point. Electrical conductivity and 1H NMR concentration scans indicate a difference in physicochemical behavior between higher and lower homologues in both the PhenCx and CyclohexCx series. Surface tension measurements with compounds belonging to either group gave typical Gibbs adsorption profiles, having d log(cac)/dn curves consistent with limiting headgroup areas in the region of (35–55 Å2) indicating monolayer formation. SANS profiles showed no evidence for aggregates below the electrical conductivity determined cac values, inferring an “on–off” mode of aggregation. Analyses of SANS profiles was consistent with charged ellipsoidal aggregates, persisting from lower through to higher homologues in both the PhenCx and CyclohexCx series
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effects of structure variation on solution properties of hydrotropes phenyl versus cyclohexyl chain tips
Langmuir, 2012Co-Authors: Marios Hopkins Hatzopoulos, Julian Eastoe, Peter J Dowding, Isabelle Grillo, Bruno Deme, Sarah E Rogers, Richard K Heenan, Robert DyerAbstract:The physicochemical behavior of the phenyl-n-alkanoate (PhenCx) and cyclohexyl-n-alkanoate (CyclohexCx) series has been investigated, supporting previous work on the understanding of hydrotropes (Hopkins Hatzopoulos, M.; Eastoe, J.; Dowding, P.J.; Rogers, S. E.; Heenan, R.; Dyer, R. Langmuir2011, 27, 12346–12353). Electrical conductivity, surface tension, 1H NMR, and small-angle neutron scattering (SANS) were used to study adsorption and aggregation in terms of critical aggregation concentration (cac). The PhenCx series exhibited very similar d log(cac)/dn to n-alkylbenzoates (CnBenz), exhibiting two branches of behavior, with a common inflection point at four linear carbons, whereas the CyclohexCx series showed no break point. Electrical conductivity and 1H NMR concentration scans indicate a difference in physicochemical behavior between higher and lower homologues in both the PhenCx and CyclohexCx series. Surface tension measurements with compounds belonging to either group gave typical Gibbs adsorption...
