scholarly journals The Correlation Production in Thermodynamics

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 111 ◽  
Author(s):  
Sheng-Wen Li
Keyword(s):  
Open System ◽  
Open Systems ◽  
Boltzmann Distribution ◽  
Ideal Gas ◽  
Many Body ◽  
Particle Collisions ◽  
Von Neumann ◽  
Entropy Increase ◽  
Many Body Systems ◽  
The Many

Macroscopic many-body systems always exhibit irreversible behaviors. However, in principle, the underlying microscopic dynamics of the many-body system, either the (quantum) von Neumann or (classical) Liouville equation, guarantees that the entropy of an isolated system does not change with time, which is quite confusing compared with the macroscopic irreversibility. We notice that indeed the macroscopic entropy increase in standard thermodynamics is associated with the correlation production inside the full ensemble state of the whole system. In open systems, the irreversible entropy production of the open system can be proved to be equivalent with the correlation production between the open system and its environment. During the free diffusion of an isolated ideal gas, the correlation between the spatial and momentum distributions is increasing monotonically, and it could well reproduce the entropy increase result in standard thermodynamics. In the presence of particle collisions, the single-particle distribution always approaches the Maxwell-Boltzmann distribution as its steady state, and its entropy increase indeed indicates the correlation production between the particles. In all these examples, the total entropy of the whole isolated system keeps constant, while the correlation production reproduces the irreversible entropy increase in the standard macroscopic thermodynamics. In this sense, the macroscopic irreversibility and the microscopic reversibility no longer contradict with each other.

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

scholarly journals GEOMETRIC PHASES AND QUANTUM PHASE TRANSITIONS

2008 ◽  
Vol 22 (06) ◽  
pp. 561-581 ◽  
Author(s):  
SHI-LIANG ZHU
Keyword(s):  
Phase Transitions ◽  
Geometric Phase ◽  
Quantum Phase Transitions ◽  
Condensed Matter ◽  
Quantum Phase ◽  
Many Body ◽  
Scientific Communities ◽  
Geometric Phases ◽  
Many Body Systems ◽  
The Many

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed the so-called "criticality of geometric phase", in which the geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of the geometric quantities may open attractive avenues and fruitful dialogue between different scientific communities.

scholarly journals Quantum Lattice-Gas Models for the Many-Body Schrödinger Equation

1997 ◽  
Vol 08 (04) ◽  
pp. 705-716 ◽  
Author(s):  
Bruce M. Boghosian ◽  
Washington Taylor
Keyword(s):  
Schrödinger Equation ◽  
Arbitrary Number ◽  
Schrodinger Equation ◽  
Lattice Gas ◽  
Quantum Computer ◽  
Many Body ◽  
Lattice Gas Models ◽  
Many Body Systems ◽  
The Many ◽  
Classical Computer

A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrödinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an exponential speedup over analogous simulations on classical computers. On a classical computer, these models give an explicitly unitary and local prescription for discretizing the Schrödinger equation. It is shown that models of this type can be constructed for an arbitrary number of particles moving in an arbitrary number of dimensions with an arbitrary interparticle interaction.

scholarly journals ENTANGLEMENT PROPERTIES OF QUANTUM MANY-BODY WAVE FUNCTIONS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4041-4057
Author(s):  
J. W. CLARK ◽  
A. MANDILARA ◽  
M. L. RISTIG ◽  
K. E. KÜRTEN
Keyword(s):  
Quantum Phase Transitions ◽  
Body Wave ◽  
Wave Functions ◽  
Von Neumann Entropy ◽  
Many Body ◽  
Lattice Systems ◽  
Bipartite Entanglement ◽  
Von Neumann ◽  
Many Body Systems ◽  
The One

The entanglement properties of correlated wave functions commonly employed in theories of strongly correlated many-body systems are studied. The variational treatment of the transverse Ising model within correlated-basis theory is reviewed, and existing calculations of the one- and two-body reduced density matrices are used to evaluate or estimate established measures of bipartite entanglement, including the Von Neumann entropy, the concurrence, and localizable entanglement, for square, cubic, and hypercubic lattice systems. The results discussed in relation to the findings of previous studies that explore the relationship of entanglement behaviors to quantum critical phenomena and quantum phase transitions. It is emphasized that Jastrow-correlated wave functions and their extensions contain multipartite entanglement to all orders.

PHILIPPE NOZIÈRES: FEENBERG MEDALIST 2001: MICROSCOPIC AND PHENOMENOLOGICAL FOUNDATIONS OF THE THEORY OF QUANTUM MANY-BODY SYSTEMS PHILIPPE NOZIÈRES REPLIES

2003 ◽  
Vol 17 (28) ◽  
pp. 4947-4952
Author(s):  
A. J. LEGGETT ◽  
E. KROTSCHECK ◽  
J. W. NEGELE
Keyword(s):  
Fermi Liquid ◽  
Single Channel ◽  
Landau Theory ◽  
Liquid Mixtures ◽  
Many Body ◽  
Many Body Theory ◽  
Temperature Solution ◽  
Many Body Systems ◽  
The Many ◽  
Solid Liquid

The Eighth Eugene Feenberg Medal is awarded to Philippe Nozières in recognition of his many pathbreaking contributions to many-body theory, including • His definitive work on the properties of the free electron gas, in particular in the region of realistic metallic densities, • his rigorous development of the theory of a normal Fermi liquid, which provided a firm microscopic foundation for the Landau theory, • his analysis of the nonequilibrium thermodynamics of 3-He solid-liquid mixtures, • his exact solution to the X-ray edge problem, • his elegant formulation of the low-temperature solution to the single-channel Kondo problem in the language of Fermi-liquid theory, • his introduction of the many-channel problem as a new class of quantum impurity systems, and • his innovative work on the static and dynamic behavior of the liquid-solid interface.

On Energy Differences in Many Body Systems

1983 ◽  
Vol 38 (12) ◽  
pp. 1276-1284
Author(s):  
Eberhard. E. Müller ◽  
Wolfgang Feist
Keyword(s):  
Relative Entropy ◽  
Von Neumann Algebras ◽  
Standard Form ◽  
Energy Operator ◽  
Many Body ◽  
Small Energy ◽  
Von Neumann ◽  
Many Body Systems

Abstract Number-and operator-valued energy differences in von Neumann algebras are discussed by means of the Tomita-Takesaki theory. Small energy differences can be evaluated by the anti-commutator of a sort of relative entropy operator and the energy operator. The New-Tamm-Dancoff procedure is studied in terms of the standard form.

scholarly journals REDUCED DENSITY MATRIX AND ENTANGLEMENT ENTROPY OF PERMUTATIONALLY INVARIANT QUANTUM MANY-BODY SYSTEMS

2012 ◽  
Vol 26 (27n28) ◽  
pp. 1243009 ◽  
Author(s):  
VLADISLAV POPKOV ◽  
MARIO SALERNO
Keyword(s):  
Density Matrix ◽  
Entanglement Entropy ◽  
Reduced Density Matrix ◽  
Diagonal Form ◽  
Temperature Phase ◽  
Many Body ◽  
Permutational Symmetry ◽  
Von Neumann ◽  
Many Body Systems ◽  
Reduced Density

In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantification of the entanglement in terms of the von Neumann (VNE), Renyi and Tsallis entropies. In particular, we show, on the specific example of the spin 1/2 Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number k fixing the polarization in the subsystem conservation of Sz and with respect to the irreducible representations of the Sn group. Analytical expression for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the Rényi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.

QUASICLASSICAL FOURIER PATH INTEGRAL QUANTUM CORRECTION TERMS TO THE KINETIC ENERGY OF INTERACTING QUANTUM MANY-BODY SYSTEMS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 3979-3991
Author(s):  
K. A. GERNOTH
Keyword(s):  
Monte Carlo ◽  
Kinetic Energy ◽  
Path Integral ◽  
Quantum Correction ◽  
Many Body ◽  
Quantum Distribution ◽  
Many Body Systems ◽  
The Many ◽  
Correction Terms ◽  
Integral Quantum

A quasiclassical expression for the kinetic energy of interacting quantum many-body systems is derived from the full quantum expression for the kinetic energy as derived by means of the Fourier path integral representation of the canonical many-body density matrix of such systems. This quasiclassical form of the kinetic energy may be cast in the shape of thermodynamic expectation values w.r.t. to the classical Boltzmann distribution of the many-body system, which involves only the many-body interaction in contrast to the full Fourier path integral quantum distribution, which carries contributions also from the many-body kinetic energy operator. The quasiclassical quantum correction terms to the classical Boltzmann equipartition value are valid when the product of temperature and particle mass is large and then lead to significant technical simplifications and increase of speed of Monte Carlo computations of the quantum kinetic energy. The formal findings are tested numerically in quantum Fourier path integral versus classical Monte Carlo simulations.

Temperature and heat

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Equations Of State ◽  
Open Systems ◽  
Boltzmann Distribution ◽  
Ideal Gas ◽  
Heat Energy ◽  
Conservation Of Energy ◽  
Temperature Scales ◽  
Ideal Gas Law ◽  
Molecular Interpretation ◽  
The Ideal

Concepts of temperature, temperature scales and temperature measurement. The ideal gas law, Dalton’s law of partial pressure. Assumptions underlying the ideal gas, and distinction between ideal and real gases. Introduction to equations-of-state such as the van der Waals, Dieterici, Berthelot and virial equations, which describe real gases. Concept of heat, and distinction between heat and temperature. Experiments of Rumford and Joule, and the principle of the conservation of energy. Units of measurement for heat. Heat as a path function. Flow of heat down a temperature gradient as an irreversible and unidirectional process. ‘Zeroth’ Law of Thermodynamics. Definitions of isolated, closed and open systems, and of isothermal, adiabatic, isobaric and isothermal changes in state. Connection between work and heat, as illustrated by the steam engine. The molecular interpretation of heat, energy and temperature. The Boltzmann distribution. Meaning of negative temperatures.

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