By Fabio Benatti
The top subject matter of the booklet is complexity in quantum dynamics. This factor is addressed through comparability with the classical ergodic, info and algorithmic complexity theories.
Of specific value is the idea of Kolmogorov-Sinai dynamical entropy and of its inequivalent quantum extensions formulated by way of Connes, Narnhofer and Thirring on one hand and Alicki and Fannes at the different. Their connections with extensions to quantum platforms of Kolmogorov-Chaitin-Solomonoff algorithmic complexity idea is additionally provided. The technical instruments hired are these of the algebraic method of quantum statistical mechanics which deals a unifying view of classical and quantum dynamical structures. Proofs and examples are supplied to be able to make the presentation self consistent.
Read or Download Quantum Entropies: Dynamics, Information and Complexity PDF
Best thermodynamics books
CRC Handbook of Liquid-Liquid Equilibrium Data of Polymer Solutions
Thermodynamic information shape the foundation for separation strategies utilized in various fields of technological know-how and undefined, from uniqueness chemical compounds to meals and prescribed drugs. One main issue to constructing new construction techniques, items, or optimization is the inability, or inaccessibility, of experimental facts concerning section equilibrium.
Thermodynamics of systems in nonequilibrium states
Approximately me -- the recent proposal : entropy and generated entropy -- The previous thought : the speed of entropy new release [reprint of the author's Thermodynamics of regular states] -- principles concerning the outdated notion : reprinted papers -- In-press addendum to ebook 1, part 14
Quantum Entropies: Dynamics, Information and Complexity
The prime subject of the publication is complexity in quantum dynamics. This factor is addressed by way of comparability with the classical ergodic, info and algorithmic complexity theories. Of specific significance is the concept of Kolmogorov-Sinai dynamical entropy and of its inequivalent quantum extensions formulated by way of Connes, Narnhofer and Thirring on one hand and Alicki and Fannes at the different.
- Numerical Continuum Mechanics
- Chemical Thermodynamics - Advanced Applications
- Fundamentals of Heat and Mass Transfer (6th Edition)
- Handbook of Numerical Heat Transfer
- Thermodynamik
Additional info for Quantum Entropies: Dynamics, Information and Complexity
Sample text
4 (von Neumann Ergodic Theorem). Let UT be the unitary Koopman operator acting on the Hilbert space H := L2μ (X ) of a dynamical triplet (X , T, μ), with T invertible. Let At : H → H be defined t−1 1 by At | ψ := U s | ψ , ψ ∈ H, and let P project onto the subspace K t s=0 T of vectors such that UT | ψ = | ψ . 1) of the sequence of operators At , P = s − limt→+∞ At . Proof: The subspace orthogonal to K is (UT − 1l)H; thus, for any ψ ∈ H, | ψ = P | ψ + (1l − P )| ψ = P | ψ + (UT − 1l)| φ , for some φ ∈ H.
Condition ii) expresses the fact that cylinder sets C[p,q] with p, q ∈ Z generate Σ, while in condition iii), C−n] = Tσ−j (C{0} ) n≥0 n≥0 j≥n denotes the largest σ-algebra, called tail of C{0} (Tail C{0} ) contained in all C−n] with n ≥ 0. [p,p+q] Cylinders in C−n] are of the form Ci(q+1) with p ≥ n , q ≥ 0; they become subsets of Tail C{0} when t → +∞. 3, one deduces that the characteristic functions of these atoms [0,q] go into the constant functions μ(Ci(q+1) ) 1l, asymptotically, whence condition iii).
4 (von Neumann Ergodic Theorem). Let UT be the unitary Koopman operator acting on the Hilbert space H := L2μ (X ) of a dynamical triplet (X , T, μ), with T invertible. Let At : H → H be defined t−1 1 by At | ψ := U s | ψ , ψ ∈ H, and let P project onto the subspace K t s=0 T of vectors such that UT | ψ = | ψ . 1) of the sequence of operators At , P = s − limt→+∞ At . Proof: The subspace orthogonal to K is (UT − 1l)H; thus, for any ψ ∈ H, | ψ = P | ψ + (1l − P )| ψ = P | ψ + (UT − 1l)| φ , for some φ ∈ H.