IQI Weekly Seminar

Entropy, majorization and thermodynamics in quantum theory and beyond

Howard Barnum, University of New Mexico,

Great progress has recently been made in understanding thermodynamics

beyond macroscopic limits by developing quantum thermodynamics as a

resource theory, describing what state transitions are possible given

specified thermodynamic resources. Thermodynamics has been cited as

one of the most robust aspects of physical theory; for example, it has

made the transition from classical to quantum. I report preliminary

results in an investigation of simple, physically meaningful

properties of a physical theory that underly the possibility of such a

thermodynamic resource theory, by studying quantum thermodynamics

within the broader realm of "general probabilistic theories". Four

such physical properties were shown by Barnum, Mueller, and Ududec to

give rise to the finite-dimensional quantum framework of density

matrices and positive operator valued measures: they are (1) abstract

spectrality (2) strong symmetry (3) no higher-order interference and

(4) energy observability. I will explain this result and discuss

whether or not all four are needed for a reasonable thermodynamics.

With a slight strengthening of (1), to unique spectrality, and a

significant weakening of (2), to the conjunction of (a) projectivity

(an abstraction of certain aspects of the quantum projection postulate

(Lüders' version)) and (b) symmetry of transition probabilities under

exchange of states with the unique finegrained effects they make

certain, we have the property, important in quantum thermodynamics,

that the outcome probabilities for any fine-grained measurement are

majorized by the spectrum of a state, and hence that

measurement-probability-based generalizations of classical

entropy-like functions are given by the classical function applied to

the spectrum.

This is joint work with Markus Mueller and Cozmin Ududec (characterization

of quantum formalism) and with Jonathan Barrett, Marius Krumm, and Markus

Mueller (thermodynamics).

http://arxiv.org/abs/1508.03107 http://arxiv.org/abs/1403.4147

For more information, please contact Jackie O'Sullivan by phone at 626.395.4964 or by email at [email protected].