Large Grants
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Previous Programs

2016 Physics of the Observer
2016 Awardees

2015 The Physics of What Happens
2015 Awardees

2013 Physics of Information
2013 Awardees

2010 The Nature of Time
2010 Awardees

2008 Foundational Questions in Physics and Cosmology
2008 Awardees

2006 Foundational Questions in Physics and Cosmology
2006 Awardees

Jonathan Barrett
University of Oxford


Matthew Leifer

Project Title

Thermodynamic vs information theoretic entropies in probabilistic theories

Project Summary

Time has a direction, in the sense that many processes happen one way but not in the reverse. A coffee mug may fall and smash into pieces, but a collection of pieces does not spontaneously leap from the floor and assemble themselves into a mug. This is a consequence of the Second Law of Thermodynamics, which states that if a system is not interfered with, entropy increases, i.e., the system becomes more disordered. The concept of entropy also appears in information theory, where it quantifies the extent to which data can be compressed. These might look like completely different concepts: what has the compression of data got to do with smashed mugs? But it turns out that they are closely linked. For example, Landauer's Principle states that if information stored in a system is erased, then the environment surrounding the system must become more disordered. The aim of the project is to investigate how entropy should be defined in a completely arbitrary probabilistic theory. The project will thereby determine whether different notions of entropy are necessarily the same, or whether their relationship is a special feature of classical and quantum theories.

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