Lindblad's P-entropy and its modern analogs

by Erik Aurell (KTH)

Thursday 25 May 2023, 13:00 → 15:00 Europe/Stockholm

AlbaNova C4:3059 - Café Planck (AlbaNova Main Building)

Göran Lindblad in his monograph "Non-Equilibrium Entropy and Irreversibility" (D. Reidel, 1983) introduced a concept he called P-entropy, as a candidate for an entropy functional for non-equilibrium states.

I will define Lindblad's P-entropy and describe the entropy-like properties which Lindblad demonstrated for this quantity.

P-entropy for an arbitrary quantum state is in essence a optimal distance from that state to the set of Gibbs states, at any temperature. Such minimal distances have become important in modern statistical physics. For classical stochastic overdamped motion Lindblad's P-entropy is equivalent to the Monge-Kantorovich transport distance (or earth-mover distance), which enters into finite-time corrections to the Landauer principle [1].

I will survey the recent literature, primarily [2] and references cited therein, and discuss when and for which models Lindblad's P-entropy can similarly be identified with variants of the (quantum) Wasserstein transport distance. The talk is based on a review prepared for the Lindblad memorial volume, available as [3].  

[1] E. Aurell, K. Gawedzki, C. Mejia-Monasterio, R. Mohayaee, P. Muratore-Ginanneschi, J. Stat. Phys. vol 147 (2012), 487.

[2] T. Van Vu and K. Saito, Phys. Rev. X vol 13 (2023), 011013.

[3] E. Aurell, R. Kawai "A perspective on Lindblad's Non-Equilibrium Entropy", arXiv:2305.07326 (2023)

 

G. Lindblad, Non-Equilibrium Entropy and Irreversibility, D. Reidel, 1983.G. Lindblad, Non-Equilibrium Entropy and Irreversibility, D. Reidel, 1983 G. Lindblad, Non-Equilibrium Entropy and Irreversibility, D. Reidel, 1983