We derive an expression for the fluctuations of the energy in an open quantum system undergoing a nontrivial evolution. The statistics of energy are constructed by means of a two-point measurement process when the system has been evolved by a completely positive and trace-preserving map. The statistics depend only on the state of the system and the dynamical map generating the evolution. In particular, we consider the Tasaki–Crooks fluctuation theorem, where a unitary evolution is replaced by a quantum channel. Our construction of a backward process using an ancilla sheds important light on the mathematical structure at play when nonunital channels are considered in quantum thermodynamics.
References
1.
M.
Esposito
, U.
Harbola
, and S.
Mukamel
, Rev. Mod. Phys.
81
, 1665
(2009
).2.
M.
Campisi
, P.
Hänggi
, and P.
Talkner
, Rev. Mod. Phys.
83
, 771
(2011
).3.
4.
P.
Hänggi
and P.
Talkner
, Nat. Phys.
11
, 108
(2015
).5.
J.
Goold
, M.
Huber
, A.
Riera
, L.
del Rio
, and P.
Skrzypczyk
, J. Phys. A
49
, 143001
(2016
).6.
S.
Vinjanampathy
and J.
Anders
, Contemp. Phys.
57
, 545
(2016
).7.
G.
Lindblad
, Non-Equilibrium Entropy and Irreversibility
(Reidal Publishing Company
, Dordrecht
, 1983
).8.
H.-P.
Breuer
and F.
Petruccione
, The Theory of Open Quantum Systems
(Oxford University
, New York
, 2002
).9.
10.
R.
Chetrite
and K.
Mallick
, J. Stat. Phys.
148
, 480
(2012
).11.
12.
H.
Spohn
and J. L.
Lebowitz
, Adv. Chem. Phys
38
, 109
(1978
).13.
E.
Davies
and H.
Spohn
, J. Stat. Phys.
19
, 511
(1978
).14.
C.
Jarzynski
, Annu. Rev. Condens. Matter Phys.
2
, 329
(2011
).15.
C.
Jarzynski
, Phys. Rev. Lett.
78
, 2690
(1997
).16.
C.
Jarzynski
, J. Stat. Mech.
2004
, P09005
.17.
G. E.
Crooks
, Phys. Rev. E
60
, 2721
(1999
).18.
H.
Tasaki
, arXiv:cond-mat/0009244 (2000
).19.
J.
Kurchan
, arXiv:cond-mat/0007360 (2000
).20.
S.
Mukamel
, Phys. Rev. Lett.
90
, 170604
(2003
).21.
P.
Talkner
, E.
Lutz
, and P.
Hänggi
, Phys. Rev. E
75
, 050102
(2007
).22.
O.-P.
Saira
, Y.
Yoon
, T.
Tanttu
, M.
Möttönen
, D. V.
Averin
, and J. P.
Pekola
, Phys. Rev. Lett.
109
, 180601
(2012
).23.
R.
Dorner
, S. R.
Clark
, L.
Heaney
, R.
Fazio
, J.
Goold
, and V.
Vedral
, Phys. Rev. Lett.
110
, 230601
(2013
).24.
L.
Mazzola
, G.
De Chiara
, and M.
Paternostro
, Phys. Rev. Lett.
110
, 230602
(2013
).25.
T. B.
Batalhão
et al, Phys. Rev. Lett.
113
, 140601
(2014
).26.
J.
Goold
, U.
Poschinger
, and K.
Modi
, Phys. Rev. E
90
, 020101(R)
(2014
).27.
J. P. S.
Peterson
, R. S.
Sarthour
, A. M.
Souza
, I. S.
Oliveira
, J.
Goold
, K.
Modi
, D. O.
Soares-Pinto
, and L. C.
Céleri
, Proc. R. Soc. A
472
, 20150813
(2016
).28.
S.
An
, J.-N.
Zhang
, M.
Um
, D.
Lv
, Y.
Lu
, J.
Zhang
, Z.-Q.
Yin
, H.
Quan
, and K.
Kim
, Nat. Phys.
11
, 193
(2015
).29.
F.
Cerisola
, Y.
Margalit
, S.
Machluf
, A. J.
Roncaglia
, J. P.
Paz
, and R.
Folman
, Nat. Commun.
8
, 1241
(2017
).30.
W.
De Roeck
and C.
Maes
, Phys. Rev. E
69
, 026115
(2004
).31.
M.
Esposito
and S.
Mukamel
, Phys. Rev. E
73
, 046129
(2006
).32.
M.
Campisi
, P.
Talkner
, and P.
Hänggi
, Phys. Rev. Lett.
102
, 210401
(2009
).33.
P.
Talkner
, M.
Campisi
, and P.
Hänggi
, J. Stat. Mech.
2009
, P02025
.34.
D.
Kafri
and S.
Deffner
, Phys. Rev. A
86
, 044302
(2012
).35.
V.
Vedral
, J. Phys. A
45
, 272001
(2012
).36.
37.
T.
Albash
, D. A.
Lidar
, M.
Marvian
, and P.
Zanardi
, Phys. Rev. E
88
, 032146
(2013
).38.
A. E.
Rastegin
and K.
Życzkowski
, Phys. Rev. E
89
, 012127
(2014
).39.
J.
Goold
, M.
Paternostro
, and K.
Modi
, Phys. Rev. Lett.
114
, 060602
(2015
).40.
G.
Manzano
, J. M.
Horowitz
, and J. M. R.
Parrondo
, Phys. Rev. E
92
, 032129
(2015
).41.
A.
Smith
, Y.
Lu
, S.
An
, X.
Zhang
, J.-N.
Zhang
, Z.
Gong
, H.
Quan
, C.
Jarzynski
, and K.
Kim
, New J. Phys.
20
, 013008
(2018
).42.
G. E.
Crooks
, Phys. Rev. A
77
, 034101
(2008
).43.
E.
Aurell
, J.
Zakrzewski
, and K.
Życzkowski
, J. Phys. A
48
, 38FT01
(2015
).44.
G. E.
Crooks
, J. Stat. Phys.
90
, 1481
(1998
).45.
S.
Milz
, F.
Pollock
, and K.
Modi
, Open Sys. Inf. Dyn.
24
, 1740016
(2017
).46.
S.
Deffner
and E.
Lutz
, Phys. Rev. Lett.
105
, 170402
(2010
).47.
F.
Binder
, S.
Vinjanampathy
, K.
Modi
, and J.
Goold
, Phys. Rev. E
91
, 032119
(2015
).48.
G.
Chiribella
, E.
Aurell
, and K.
Życzkowski
, Phys. Rev. Res.
3
, 033028
(2021
).49.
P.
Taranto
, K.
Modi
, and F. A.
Pollock
, Phys. Rev. E
97
, 052111
(2018
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
2021
Author(s)
You do not currently have access to this content.