PIRSA:13040112 Scientific Series Quantum Foundations

DOI10.48660/13040112

Series: Perimeter Institute Quantum Discussions

Dahlsten, O. (2013). Laws of thermodynamics beyond the von Neumann regime. Perimeter Institute. https://pirsa.org/13040112

Dahlsten, Oscar. Laws of thermodynamics beyond the von Neumann regime. Perimeter Institute, Apr. 29, 2013, https://pirsa.org/13040112 

@misc{ pirsa_PIRSA:13040112,
  doi = {10.48660/13040112},
  url = {https://pirsa.org/13040112},
  author = {Dahlsten, Oscar},
  keywords = {Quantum Foundations},
  language = {en},
  title = {Laws of thermodynamics beyond the von Neumann regime},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {apr},
  note = {PIRSA:13040112 see, \url{https://pirsa.org}}
}

Abstract

A recent development in information theory is the generalisation of quantum Shannon information theory to the operationally motivated smooth entropy information theory, which originates in quantum cryptography research. In a series of papers the first steps have been taken towards creating a statistical mechanics based on smooth entropy information theory. This approach turns out to allow us to answer questions one might not have thought were possible in statistical mechanics, such as how much work one can extract in a given realisation, as a function of the failure-probability. This is in contrast to the standard approach which makes statements about average work. Here we formulate the laws of thermodynamics that this new approach gives rise to. We show in particular that the Second Law needs to be tightened. The new laws are motivated by our main quantitative result which states how much work one can extract or must invest in order to affect a given state change with a given probability of success. For systems composed of very large numbers of identical and uncorrelated subsystems, which we call the von Neumann regime, we recover the standard von Neumann entropy statements.

Joint work with Egloff, Renner and Vedral

http://arxiv.org/abs/1207.0434

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