Thermodynamics from relative entropy.

@article{Floerchinger2020ThermodynamicsFR,
  title={Thermodynamics from relative entropy.},
  author={Stefan Floerchinger and Tobias Haas},
  journal={Physical review. E},
  year={2020},
  volume={102 5-1},
  pages={
          052117
        }
}
Thermodynamics can be developed from a microscopic starting point in terms of entropy and the maximum entropy principle. We investigate here to what extent one can replace entropy with relative entropy which has several advantages, for example, in the context of local quantum field theory. We find that the principle of maximum entropy can be replaced by a principle of minimum expected relative entropy. Various ensembles and their thermodynamic potentials can be defined through relative entropy… Expand

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References

SHOWING 1-10 OF 115 REFERENCES
Boltzmann entropy, relative entropy, and related quantities in thermodynamic space
The conventional solution methods for the Boltzmann kinetic equation such as the Chapman–Enskog method or the moment method provide a thermodynamic branch of the distribution function evolvingExpand
Relative entropies in conformal field theory.
TLDR
A Euclidean path-integral approach to Renyi relative entropies in conformal field theory is constructed, then the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature are computed using a replica trick. Expand
Relative entropy and the Bekenstein bound
Elaborating on a previous work by Marolf et al, we relate some exact results in quantum field theory and statistical mechanics to the Bekenstein universal bound on entropy. Specifically, we considerExpand
Entanglement entropy, entropy production and time evolution in high energy QCD
Abstract Working in the framework of the Color Glass Condensate effective theory of high energy QCD, we revisit the momentum space entanglement entropy of the soft gluons produced in high energyExpand
The role of relative entropy in quantum information theory
Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately, it has emerged that they areExpand
Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction
We review the fundamental properties of the quantum relative entropy for finite-dimensional Hilbert spaces. In particular, we focus on several inequalities that are related to the second law ofExpand
Relative Entropy of States of von Neumann Algebras
Relative entropy of two states of a von Neumann algebra is defined in terms of the relative modular operator. The strict positivity, lower semicontinuity, convexity and monotonicity of relativeExpand
Local temperatures and local terms in modular Hamiltonians
We show there are analogues to the Unruh temperature that can be defined for any quantum field theory and region of the space. These local temperatures are defined using relative entropy withExpand
Quantum source of entropy for black holes.
We associate to any quantum field propagating in the background metric of a black hole an effective density matrix whose statistical entropy can be interpreted as a contribution to the total entropyExpand
Towards a derivation of holographic entanglement entropy
We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observingExpand
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