# The Role of Quantum Information in Thermodynamics

**Exemplary illustration of different notions of the unitary orbit of equilibrium states. Two Gibbs states (represented by two different blue dots on the top) are transformed using a unitary operation. In a. the whole unitary orbit is explored, in b. only unitaries that change the energy by at most a fixed amount, while in c. only energy conserving unitaries with a reference system are used. Illustration taking from the review “The role of quantum information in thermodynamics”.**

The foundation of thermodynamics in statistical physics deals with fundamental bounds on state transformations that arise due to inevitably limited information. A particular focus is traditionally on the notion of transferring energy and how it divides into a useful part, often referred to as “work” and some waste “heat”. Already this distinction, often referred to as first law of thermodynamics, is highly dependent on the available information about the actual state of the system. The lack of which, quantified by different notions of entropy, is the focus of the second law of thermodynamics and beyond telling us ultimate bounds on machine performances and impossibilities of perpetua mobile, it seemingly determines the inevitable fate of our entire universe. It is thus not surprising that one of the most central objects of “classical” thermodynamics is “classical” information.

In the emerging field of quantum thermodynamics, we try to understand how and if fundamental thermodynamic laws change, when considering the nature of information to be quantum. In particular, in collaboration with groups in Barcelona, Bristol and Geneva, we are investigating the notions of heat and work for quantum systems [1], the thermodynamic value of correlations [2], the general structure of passive states [3], the impact of limited control on resources [4,6], and equilibration beyond energy as conserved quantities [5].

Recent work:

Y. Guryanova, N. Friis and M. Huber. Ideal projective measurements have infinite resource costs. Quantum 4, 222 (2020).

T. Debarba, G. Manzano, Y. Guryanova, M. Huber and N. Friis. Work estimation and work fluctuations in the presence of non-ideal measurements. New Journal of Physics 21, (2019) 113002.

N. Friis and M. Huber. Precision and work fluctuations in gaussian battery charging. Quantum 2, 61 (2018).

F. Anza, C. Gogolin and M. Huber. Eigenstate thermalization for degenerate observables. Physical review letters 120, 150603 (2018).

Bibliography:

[1] M. Perarnau-Llobet, E. Bäumer, K. V. Hovhannisyan, M. Huber, A. Acín, No-Go Theorem for the Characterisation of Work Fluctuations in Coherent Quantum Systems, Phys. Rev. Lett. 118, 070601 (2017)

[2] M.Perarnau-Llobet, K.V. Hovhannisyan, M. Huber, P. Skrzypczyk, N. Brunner, A. Acín, Extractable Work from Correlations, Phys. Rev. X 5, 041011 (2015)

[3] M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, J. Tura, A. Acín, Most energetic passive states, Phys. Rev. E 92, 042147 (2015)

[4] E. G. Brown, N. Friis, M. Huber, Passivity and practical work extraction using Gaussian operations, New J. Phys. 18, 113028 (2016)

[5] Y. Guryanova, S. Popescu, A. J. Short, R. Silva, P. Skrzypczyk, Thermodynamics of quantum systems with multiple conserved quantities, Nature Commun. 7, 12049 (2016)

[6] N. Friis, M. Huber, Precision and Work Fluctuations in Gaussian Battery Charging, arXiv:1708.00749