Entanglement and the foundations of statistical mechanics

  title={Entanglement and the foundations of statistical mechanics},
  author={Sandu Popescu and Anthony J. Short and Andreas J. Winter},
  journal={Nature Physics},
Statistical mechanics is one of the most successful areas of physics. Yet, almost 150 years since its inception, its foundations and basic postulates are still the subject of debate. Here we suggest that the main postulate of statistical mechanics, the equal a priori probability postulate, should be abandoned as misleading and unnecessary. We argue that it should be replaced by a general canonical principle, whose physical content is fundamentally different from the postulate it replaces: it… 

Entanglement and thermodynamics in general probabilistic theories

This work addresses the question whether an entangled state can be transformed into another by means of local operations and classical communication and proves a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement.

Pure state quantum statistical mechanics

The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective

Information-theoretic foundations of thermodynamics in general probabilistic theories

In this thesis we study the informational underpinnings of thermodynamics and statistical mechanics. To this purpose, we use an abstract framework— general probabilistic theories—, capable of

Pure states statistical mechanics: On its foundations and applications to quantum gravity

The project concerns the study of the interplay among quantum mechanics, statistical mechanics and thermodynamics, in isolated quantum systems. The goal of this research is to improve our

Information-theoretic equilibrium and observable thermalization

A new notion of thermal equilibrium is proposed, focused on observables rather than on the full state of the quantum system, and it is shown that there is always a class of observables which exhibits thermal equilibrium properties and a recipe to explicitly construct them.

Perspectives on the Formalism of Quantum Theory

Quantum theory has the distinction among physical theories of currently underpinning most of modern physics, while remaining essentially mysterious, with no general agreement about the nature of its

Thermodynamic functionality of autonomous quantum networks

Thermodynamics is a theory of impressive success and a wide range of applicability. Nevertheless, it took about two hundred years after the basic formulation of phenomenological thermodynamics until

Thermodynamics and the structure of quantum theory

This work studies how compatibility with thermodynamics constrains the structure of quantum theory by studying how self-duality and analogues of projective measurements, subspaces and eigenvalues imply important aspects ofquantum theory.

Understanding Equipartition and Thermalization from Decoupling

The decoupling technique was originally developed for information-theoretical purposes. It describes the conditions under which the correlations in a bipartite state disappear if one part undergoes

Foundations of statistical mechanics from symmetries of entanglement

Envariance—entanglement assisted invariance—is a recently discovered symmetry of composite quantum systems. We show that thermodynamic equilibrium states are fully characterized by their envariance.



From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example

Derivation of the canonical (or Boltzmann) distribution based only on quantum dynamics is discussed. Consider a closed system which consists of a mutually interacting subsystem and a heat bath, and

Aspects of Generic Entanglement

We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the ``concentration

Non-Markovian quantum dynamics: correlated projection superoperators and Hilbert space averaging.

It is shown that the application of the TCL technique to this class of correlated superoperators enables the nonperturbative treatment of the dynamics of system-environment models for which the standard approach fails in any finite order of the coupling strength.

Partial quantum information

The concept of prior quantum information is explored: given an unknown quantum state distributed over two systems, how much quantum communication is needed to transfer the full state to one system is determined, conditioned on its prior information.

Thermalization of quantum systems by finite baths

We consider a discrete quantum system coupled to a finite bath, which may consist of only one particle, in contrast to the standard baths which usually consist of continua of oscillators, spins, etc.

Average Entropy of a Quantum Subsystem.

  • Sen
  • Mathematics
    Physical review letters
  • 1996
It was recently conjectured by D. Page that if a quantum system of Hilbert space dimension {ital nm} is in a random pure state then the average entropy of a subsystem of dimension {ital m} where

Quantum computation and quantum information

This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.

Entropy of an n‐system from its correlation with a k‐reservoir

Let a random pure state vector be chosen in nk‐dimensional Hilbert space, and consider an n‐dimensional subsystem’s density matrix P. P will usually be close to the totally unpolarized mixed state if

Fourier's law from Schrödinger dynamics.

A theory is presented which predicts energy diffusion within one-dimensional chains of weakly coupled many level systems for almost all initial states, if some concrete conditions on their Hamiltonians are met.

Average entropy of a subsystem.

  • Page
  • Mathematics
    Physical review letters
  • 1993
There is less than one-half unit of information, on average, in the smaller subsystem of a total system in a random pure state.