Annual review of physical chemistry, ISSN 1545-1593, 2008, Volume 59, Issue 1, pp. 603 - 633

Fluctuation theorems, developed over the past 15 years, have resulted in fundamental breakthroughs in our understanding of how irreversibility emerges from reversible dynamics and have provided new...

Reversibility | Second law of thermodynamics | Far-from-equilibrium processes | Nonequilibrium statistical mechanics | Free energy change | far-from-equilibrium processes | STEADY-STATES | NONEQUILIBRIUM MEASUREMENTS | CHEMISTRY, PHYSICAL | nonequilibrium statistical mechanics | second law of thermodynamics | HEAT | free energy change | ENTROPY PRODUCTION | FREE-ENERGY DIFFERENCES | EQUALITY | reversibility | SYSTEMS | DYNAMICAL ENSEMBLES | Biopolymers - chemistry | Thermodynamics | Models, Chemical | Time Factors | Colloids | Chemical Phenomena | Chemistry, Physical | Research | Statistical mechanics | Analysis | Gibbs' free energy | Physics - Statistical Mechanics

Reversibility | Second law of thermodynamics | Far-from-equilibrium processes | Nonequilibrium statistical mechanics | Free energy change | far-from-equilibrium processes | STEADY-STATES | NONEQUILIBRIUM MEASUREMENTS | CHEMISTRY, PHYSICAL | nonequilibrium statistical mechanics | second law of thermodynamics | HEAT | free energy change | ENTROPY PRODUCTION | FREE-ENERGY DIFFERENCES | EQUALITY | reversibility | SYSTEMS | DYNAMICAL ENSEMBLES | Biopolymers - chemistry | Thermodynamics | Models, Chemical | Time Factors | Colloids | Chemical Phenomena | Chemistry, Physical | Research | Statistical mechanics | Analysis | Gibbs' free energy | Physics - Statistical Mechanics

Journal Article

Physical review letters, ISSN 1079-7114, 2017, Volume 119, Issue 10, p. 100601

We prove the second law of thermodynamics and the nonequilibrium fluctuation theorem for pure quantum states...

CHAOS | THERMODYNAMICS | THERMALIZATION | PHYSICS, MULTIDISCIPLINARY | ENTANGLEMENT | HEAT-GENERATION | EQUILIBRIUM | EQUALITY | DYNAMICS | RELAXATION

CHAOS | THERMODYNAMICS | THERMALIZATION | PHYSICS, MULTIDISCIPLINARY | ENTANGLEMENT | HEAT-GENERATION | EQUILIBRIUM | EQUALITY | DYNAMICS | RELAXATION

Journal Article

Physical review. E, Statistical, nonlinear, and soft matter physics, ISSN 1550-2376, 2013, Volume 88, Issue 2, p. 022147

.... We show that such difference, which we call the hidden entropy production, obeys an integral fluctuation theorem if all variables are time-reversal invariant, or if the density function is symmetric...

HEAT ENGINE | STOCHASTIC DYNAMICS | THERMODYNAMICS | PHYSICS, FLUIDS & PLASMAS | FREE-ENERGY DIFFERENCES | EQUALITY | SYSTEMS | DIFFUSION | PHYSICS, MATHEMATICAL | Physics - Statistical Mechanics

HEAT ENGINE | STOCHASTIC DYNAMICS | THERMODYNAMICS | PHYSICS, FLUIDS & PLASMAS | FREE-ENERGY DIFFERENCES | EQUALITY | SYSTEMS | DIFFUSION | PHYSICS, MATHEMATICAL | Physics - Statistical Mechanics

Journal Article

Acta Mechanica, ISSN 0001-5970, 9/2016, Volume 227, Issue 9, pp. 2439 - 2449

... fractional conserved quantity is given. Finally, the Noether’s theorem for the fractional Birkhoffian system of variable order is established...

Engineering | Vibration, Dynamical Systems, Control | Engineering Thermodynamics, Heat and Mass Transfer | Theoretical and Applied Mechanics | Continuum Mechanics and Mechanics of Materials | Structural Mechanics | Classical Continuum Physics | MECHANICS | VARIATIONAL-PROBLEMS | SYMMETRIES | DERIVATIVES | Studies | Theory | Calculus | Theorems | Transformations | Derivatives | Invariance | Mathematical analysis | Symmetry

Engineering | Vibration, Dynamical Systems, Control | Engineering Thermodynamics, Heat and Mass Transfer | Theoretical and Applied Mechanics | Continuum Mechanics and Mechanics of Materials | Structural Mechanics | Classical Continuum Physics | MECHANICS | VARIATIONAL-PROBLEMS | SYMMETRIES | DERIVATIVES | Studies | Theory | Calculus | Theorems | Transformations | Derivatives | Invariance | Mathematical analysis | Symmetry

Journal Article

Acta Mechanica, ISSN 0001-5970, 3/2017, Volume 228, Issue 3, pp. 901 - 917

In this paper, the generalized Noether’s theorem for continuous mechanical systems is formulated by analogy with Vujanović and Djukić’s (Acta Mech 23:17–27, 1975) and Vujanović’s...

Engineering | Vibration, Dynamical Systems, Control | Classical and Continuum Physics | Engineering Thermodynamics, Heat and Mass Transfer | Theoretical and Applied Mechanics | Continuum Mechanics and Mechanics of Materials | Structural Mechanics | NONCONSERVATIVE SYSTEMS | MECHANICS | Mechanics | Theorems | Lagrange multiplier | Integrals | Analogies | Transformations (mathematics) | Mathematical analysis | Austenitic stainless steels | Constants | Mechanical systems

Engineering | Vibration, Dynamical Systems, Control | Classical and Continuum Physics | Engineering Thermodynamics, Heat and Mass Transfer | Theoretical and Applied Mechanics | Continuum Mechanics and Mechanics of Materials | Structural Mechanics | NONCONSERVATIVE SYSTEMS | MECHANICS | Mechanics | Theorems | Lagrange multiplier | Integrals | Analogies | Transformations (mathematics) | Mathematical analysis | Austenitic stainless steels | Constants | Mechanical systems

Journal Article

Physical review letters, ISSN 1079-7114, 2017, Volume 119, Issue 25, p. 258001

Active biological systems reside far from equilibrium, dissipating heat even in their steady state, thus requiring an extension of conventional equilibrium...

HOUSEKEEPING HEAT | THERMODYNAMICS | DIFFUSION-PROCESSES | PARTICLES | PHYSICS, MULTIDISCIPLINARY | FLOCKS | HAMILTONIAN-SYSTEMS | INFORMATION | FREE-ENERGY DIFFERENCES | HYDRODYNAMICS | LANGEVIN SYSTEMS

HOUSEKEEPING HEAT | THERMODYNAMICS | DIFFUSION-PROCESSES | PARTICLES | PHYSICS, MULTIDISCIPLINARY | FLOCKS | HAMILTONIAN-SYSTEMS | INFORMATION | FREE-ENERGY DIFFERENCES | HYDRODYNAMICS | LANGEVIN SYSTEMS

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 7/2016, Volume 26, Issue 3, pp. 2425 - 2449

...)-form solution of the CR Hodge–Laplace heat equation and monotonicity of the heat equation deformation, we obtain an optimal gap theorem for a complete strictly pseudoconvex CR
$$(2n+1)$$
(
2
n
+
1...

Li–Yau–Hamilton inequality | Subelliptic operator | Heat kernel | Mathematics | Abstract Harmonic Analysis | CR Moment type estimate | Fourier Analysis | 32V20 | Secondary 53C56 | Convex and Discrete Geometry | CR Hodge–Laplace | Gap theorem | Global Analysis and Analysis on Manifolds | Primary 32V05 | Differential Geometry | Dynamical Systems and Ergodic Theory | Li-Yau-Hamilton inequality | PLURISUBHARMONIC-FUNCTIONS | VOLUME | COMPLETE KAHLER-MANIFOLDS | CR Hodge-Laplace | MATHEMATICS | UNIFORMIZATION THEOREM | CURVATURE | DIRICHLET PROBLEM | EQUATION

Li–Yau–Hamilton inequality | Subelliptic operator | Heat kernel | Mathematics | Abstract Harmonic Analysis | CR Moment type estimate | Fourier Analysis | 32V20 | Secondary 53C56 | Convex and Discrete Geometry | CR Hodge–Laplace | Gap theorem | Global Analysis and Analysis on Manifolds | Primary 32V05 | Differential Geometry | Dynamical Systems and Ergodic Theory | Li-Yau-Hamilton inequality | PLURISUBHARMONIC-FUNCTIONS | VOLUME | COMPLETE KAHLER-MANIFOLDS | CR Hodge-Laplace | MATHEMATICS | UNIFORMIZATION THEOREM | CURVATURE | DIRICHLET PROBLEM | EQUATION

Journal Article

Physical review. E, Statistical, nonlinear, and soft matter physics, ISSN 1539-3755, 11/2011, Volume 84, Issue 5, p. 051122

Carnot's theorem poses a fundamental limit on the maximum efficiency achievable from an engine that works between two reservoirs at thermal equilibrium...

LIMITS | HEAT | WORK | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | COHERENCE

LIMITS | HEAT | WORK | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | COHERENCE

Journal Article

2017, ISBN 331945725X

eBook

Calculus of variations and partial differential equations, ISSN 0944-2669, 12/2018, Volume 57, Issue 6, p. 1

.... We prove comparison theorems and a vanishing theorem related to these curvature conditions, and construct various examples to illustrate subtle relationship among...

MATHEMATICS | MATHEMATICS, APPLIED | QUADRATIC BISECTIONAL CURVATURE | HEAT-EQUATION | MONGE-AMPERE EQUATION

MATHEMATICS | MATHEMATICS, APPLIED | QUADRATIC BISECTIONAL CURVATURE | HEAT-EQUATION | MONGE-AMPERE EQUATION

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 1/2014, Volume 154, Issue 1, pp. 188 - 203

.... This new extended heat theorem holds true for arbitrary driving and does not require assumptions of local or close to equilibrium...

Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Clausius heat theorem | Physics | Nonequilibrium fluctuations | Steady state thermodynamics | PHYSICS, MATHEMATICAL | Thermodynamics | Usage | Physics - Statistical Mechanics

Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Clausius heat theorem | Physics | Nonequilibrium fluctuations | Steady state thermodynamics | PHYSICS, MATHEMATICAL | Thermodynamics | Usage | Physics - Statistical Mechanics

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 1/2016, Volume 26, Issue 1, pp. 156 - 170

...J Geom Anal (2016) 26:156–170
DOI 10.1007/s12220-014-9542-x
The Lichnerowicz–Obata Theorem on Sub-Riemannian
Manifolds with Transverse Symmetries
Fabrice...

Abstract Harmonic Analysis | Fourier Analysis | Sub-Riemannian geometry | Convex and Discrete Geometry | Obata theorem | Lichnerowicz estimate | Global Analysis and Analysis on Manifolds | 53C17 | Mathematics | Differential Geometry | Dynamical Systems and Ergodic Theory | LAPLACIAN | MATHEMATICS | QUATERNIONIC CONTACT MANIFOLD | INEQUALITIES | BOUNDS | 1ST EIGENVALUE | SUBELLIPTIC HEAT KERNEL

Abstract Harmonic Analysis | Fourier Analysis | Sub-Riemannian geometry | Convex and Discrete Geometry | Obata theorem | Lichnerowicz estimate | Global Analysis and Analysis on Manifolds | 53C17 | Mathematics | Differential Geometry | Dynamical Systems and Ergodic Theory | LAPLACIAN | MATHEMATICS | QUATERNIONIC CONTACT MANIFOLD | INEQUALITIES | BOUNDS | 1ST EIGENVALUE | SUBELLIPTIC HEAT KERNEL

Journal Article

13.
Full Text
Ergodic-Type Limit Theorem for Fundamental Solutions of Critical Schrödinger Operators

Journal of Theoretical Probability, ISSN 0894-9840, 3/2019, Volume 32, Issue 1, pp. 447 - 459

...
. In this paper, we give a certain ergodic-type limit theorem for fundamental solutions of critical Schrödinger operators.

35J10 | Feynman–Kac functional | 60J40 | Symmetric stable process | Dirichlet form | Heat kernel | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Schrödinger form | 60J45 | Criticality | Schrodinger form | BEHAVIOR | STATISTICS & PROBABILITY | FEYNMAN-KAC FUNCTIONALS | SPECTRAL FUNCTIONS | Feynman-Kac functional

35J10 | Feynman–Kac functional | 60J40 | Symmetric stable process | Dirichlet form | Heat kernel | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Schrödinger form | 60J45 | Criticality | Schrodinger form | BEHAVIOR | STATISTICS & PROBABILITY | FEYNMAN-KAC FUNCTIONALS | SPECTRAL FUNCTIONS | Feynman-Kac functional

Journal Article

Modern Physics Letters A, ISSN 0217-7323, 01/2020, Volume 35, Issue 3, p. 2040010

...., the Nernst heat theorem is satisfied, if the dc conductivity of the plate material is disregarded in calculations...

Nernst heat theorem | Casimir-Polder free energy | ASTRONOMY & ASTROPHYSICS | PHYSICS, NUCLEAR | PHYSICS, MATHEMATICAL | ferromagnetic dielectrics | PHYSICS, PARTICLES & FIELDS | Physics - Quantum Physics

Nernst heat theorem | Casimir-Polder free energy | ASTRONOMY & ASTROPHYSICS | PHYSICS, NUCLEAR | PHYSICS, MATHEMATICAL | ferromagnetic dielectrics | PHYSICS, PARTICLES & FIELDS | Physics - Quantum Physics

Journal Article

Journal of Engineering Thermophysics, ISSN 1810-2328, 10/2018, Volume 27, Issue 4, pp. 489 - 500

The paper presents a review of research dealing with the limit energy theorem for fast gas flow systems (FGFS’s) [19, 21, 23, 24, 38...

Fluid- and Aerodynamics | Thermodynamics | Physics | MATHEMATICS | HEAT | MECHANICS | THERMODYNAMICS | DEVICE | FIN | SEPARATION | INTENSIFICATION | BLACK-HOLES | ENGINEERING, MECHANICAL

Fluid- and Aerodynamics | Thermodynamics | Physics | MATHEMATICS | HEAT | MECHANICS | THERMODYNAMICS | DEVICE | FIN | SEPARATION | INTENSIFICATION | BLACK-HOLES | ENGINEERING, MECHANICAL

Journal Article

Journal of statistical physics, ISSN 1572-9613, 2019, Volume 180, Issue 1-6, pp. 263 - 296

We continue the investigation, started in Jaksic et al. in (J. Stat. Phys. 166:926-1015,2017), of a network of harmonic oscillators driven out of thermal...

NONEQUILIBRIUM STATISTICAL-MECHANICS | ENTROPIC FLUCTUATIONS | Heat fluxes | Large deviations | Entropy production | Nonequilibrium steady state | DYNAMICAL ENSEMBLES | PHYSICS, MATHEMATICAL | Fluctuation relations | Reservoirs | Mathematical Physics | Physics

NONEQUILIBRIUM STATISTICAL-MECHANICS | ENTROPIC FLUCTUATIONS | Heat fluxes | Large deviations | Entropy production | Nonequilibrium steady state | DYNAMICAL ENSEMBLES | PHYSICS, MATHEMATICAL | Fluctuation relations | Reservoirs | Mathematical Physics | Physics

Journal Article

International journal of heat and mass transfer, ISSN 0017-9310, 12/2017, Volume 115, pp. 1109 - 1120

•The theorem for the local volume average of a gradient (or a divergence) has been modified.•The governing equations for porous media is derived with the aid of the modified theorem...

Porous media | Volume averaging | Governing equation | Reynolds transport theorem | VOLUME AVERAGE | HEAT-TRANSFER | BOUNDARY-CONDITIONS | DISPERSION | CLOSURE | FLOW | ENGINEERING, MECHANICAL | MECHANICS | THERMODYNAMICS | HOMOGENEOUS FLUID | INTERFACE | TURBULENCE MODEL | SYSTEMS | Analysis | Numerical analysis

Porous media | Volume averaging | Governing equation | Reynolds transport theorem | VOLUME AVERAGE | HEAT-TRANSFER | BOUNDARY-CONDITIONS | DISPERSION | CLOSURE | FLOW | ENGINEERING, MECHANICAL | MECHANICS | THERMODYNAMICS | HOMOGENEOUS FLUID | INTERFACE | TURBULENCE MODEL | SYSTEMS | Analysis | Numerical analysis

Journal Article

Journal of Ambient Intelligence and Humanized Computing, ISSN 1868-5137, 10/2017, Volume 8, Issue 5, pp. 717 - 725

.... This paper proves an existence and uniqueness theorem of solutions for general uncertain heat equations under linear growth condition and Lipschitz condition...

Engineering | Computational Intelligence | Uncertain heat equation | User Interfaces and Human Computer Interaction | Artificial Intelligence (incl. Robotics) | Liu process | Existence and uniqueness theorem | Robotics and Automation | COMPUTER SCIENCE, INFORMATION SYSTEMS | MODEL | TELECOMMUNICATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Research | Heat equation | Existence theorems | Mathematical research

Engineering | Computational Intelligence | Uncertain heat equation | User Interfaces and Human Computer Interaction | Artificial Intelligence (incl. Robotics) | Liu process | Existence and uniqueness theorem | Robotics and Automation | COMPUTER SCIENCE, INFORMATION SYSTEMS | MODEL | TELECOMMUNICATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Research | Heat equation | Existence theorems | Mathematical research

Journal Article

Acta mechanica, ISSN 1619-6937, 2013, Volume 225, Issue 1, pp. 77 - 90

This paper focuses on studying Noether’s theorem in phase space for fractional variational problems from extended exponentially fractional integral introduced by El-Nabulsi...

Engineering | Vibration, Dynamical Systems, Control | Engineering Thermodynamics, Heat and Mass Transfer | Theoretical and Applied Mechanics | Continuum Mechanics and Mechanics of Materials | Structural Mechanics | Classical Continuum Physics | MECHANICS | SYMMETRIES | CALCULUS | LAGRANGE EQUATION | SYSTEMS | FORMULATION | HAMILTON FORMALISM | DERIVATIVES | Studies | Lagrange multiplier | Mathematical analysis | Phase transitions | Mechanical engineering | Theorems | Integrals | Group theory | Transformations | Criteria | Invariance | Symmetry

Engineering | Vibration, Dynamical Systems, Control | Engineering Thermodynamics, Heat and Mass Transfer | Theoretical and Applied Mechanics | Continuum Mechanics and Mechanics of Materials | Structural Mechanics | Classical Continuum Physics | MECHANICS | SYMMETRIES | CALCULUS | LAGRANGE EQUATION | SYSTEMS | FORMULATION | HAMILTON FORMALISM | DERIVATIVES | Studies | Lagrange multiplier | Mathematical analysis | Phase transitions | Mechanical engineering | Theorems | Integrals | Group theory | Transformations | Criteria | Invariance | Symmetry

Journal Article