The second law of thermodynamics as a deterministic theorem for quantum spin systems

@article{Wreszinski2022TheSL,
  title={The second law of thermodynamics as a deterministic theorem for quantum spin systems},
  author={Walter F. Wreszinski},
  journal={Reviews in Mathematical Physics},
  year={2022}
}
  • W. Wreszinski
  • Published 2 December 2021
  • Mathematics
  • Reviews in Mathematical Physics
We review our approach to the second law of thermodynamics as a theorem assering the growth of the mean (Gibbs-von Neumann) entropy of a class of quantum spin systems undergoing automorphic (unitary) adiabatic transformations. Non-automorphic interactions with the environment, although known to produce on the average a strict reduction of the entropy of systems with finite number of degrees of freedom, are proved to conserve the mean entropy on the average. The results depend crucially on two… 

A theory of quantum (statistical) measurement

We propose a theory of quantum (statistical) measurement which is close, in spirit, to Hepp’s theory, which is centered on the concepts of decoherence and macroscopic (classical) observables, and

References

SHOWING 1-10 OF 87 REFERENCES

Irreversibility, the time arrow and a dynamical proof of the second law of thermodynamics

  • W. Wreszinski
  • Physics
    Quantum Studies: Mathematics and Foundations
  • 2019
We provide a dynamical proof of the second law of thermodynamics, along the lines of an argument of Penrose and Gibbs, making crucial use of the upper semicontinuity of the mean entropy proved by

Mean entropy of states in classical statistical mechanics

The equilibrium states for an infinite system of classical mechanics may be represented by states over AbelianC* algebras. We consider here continuous and lattice systems and define a mean entropy

Mean Entropy of States in Quantum‐Statistical Mechanics

The equilibrium states for an infinite system of quantum mechanics may be represented by states over suitably chosen C* algebras. We consider the problem of associating an entropy with these states

On Entropy Production of Repeated Quantum Measurements II. Examples

We illustrate the mathematical theory of entropy production in repeated quantum measurement processes developed in a previous work by studying examples of quantum instruments displaying various

The Time-Evolution of States in Quantum Mechanics according to the ETH-Approach

It is argued that the Schrödinger equation does not yield a correct description of the quantum-mechanical time evolution of states of isolated physical systems featuring events. A general statistical

Galilei-Invariant Quantum Field Theories with Pair Interactions:. a Review

We exhibit a class of quantum field theories where particles interact with pair potentials and for which the time evolution exists in the Heisenberg representation. The essential condition for

Approach to equilibrium in a simple model

The time evolution of a class of generalized quantum Ising models (with various long‐range interactions, including Dyson's 1/rα) has been studied from the C*‐algebraic point of view. We establish

On the mixing property for a class of states of relativistic quantum fields

Let ω be a factor state on the quasilocal algebra A of observables generated by a relativistic quantum field, which, in addition, satisfies certain regularity conditions [satisfied by ground states
...