There is a long-standing question as to whether and to what extent it is possible to describe nonequilibrium systems in stationary states in terms of global thermodynamic functions. The positive answers have been obtained only for isothermal systems or systems with small temperature differences. We formulate thermodynamics of the stationary states of the ideal gas subjected to heat flow in the form of the zeroth, first, and second law. Surprisingly, the formal structure of steady state thermodynamics is the same as in equilibrium thermodynamics. We rigorously show that U satisfies the following equation dU = T*dS* − pdV for a constant number of particles, irrespective of the shape of the container, boundary conditions, the size of the system, or the mode of heat transfer into the system. We calculate S* and T* explicitly. The theory selects stable nonequilibrium steady states in a multistable system of ideal gas subjected to volumetric heating. It reduces to equilibrium thermodynamics when heat flux goes to zero.
REFERENCES
1.
H. B.
Callen
, Thermodynamics and An Introduction to Thermostatistics
(John Wiley & Sons
, 2006
).2.
I.
Müller
, A History of Thermodynamics: The Doctrine of Energy and Entropy
(Springer Science & Business Media
, 2007
).3.
I.
Prigogine
, Introduction to Thermodynamics of Irreversible Processes
(Interscience Publishers
, 1967
).4.
Y.
Oono
and M.
Paniconi
, “Steady state thermodynamics
,” Prog. Theor. Phys. Suppl.
130
, 29
–44
(1998
).5.
K.
Sekimoto
, “Langevin equation and thermodynamics
,” Prog. Theor. Phys. Suppl.
130
, 17
–27
(1998
).6.
T.
Hatano
and S.-i.
Sasa
, “Steady-state thermodynamics of Langevin systems
,” Phys. Rev. Lett.
86
(16
), 3463
(2001
).7.
S.-i.
Sasa
and H.
Tasaki
, “Steady state thermodynamics
,” J. Stat. Phys.
125
(1
), 125
–224
(2006
).8.
G.
Guarnieri
, D.
Morrone
, B.
Çakmak
, F.
Plastina
, and S.
Campbell
, “Non-equilibrium steady-states of memoryless quantum collision models
,” Phys. Lett. A
384
(24
), 126576
(2020
).9.
E.
Boksenbojm
, C.
Maes
, K.
Netočný
, and J.
Pešek
, “Heat capacity in nonequilibrium steady states
,” Europhys. Lett.
96
(4
), 40001
(2011
).10.
R. R.
Netz
, “Approach to equilibrium and nonequilibrium stationary distributions of interacting many-particle systems that are coupled to different heat baths
,” Phys. Rev. E
101
(2-1
), 022120
(2020
).11.
D.
Mandal
, “Nonequilibrium heat capacity
,” Phys. Rev. E
88
(6
), 062135
(2013
).12.
R.
Holyst
, A.
Maciołek
, Y.
Zhang
, M.
Litniewski
, P.
Knychała
, M.
Kasprzak
, and M.
Banaszak
, “Flux and storage of energy in nonequilibrium stationary states
,” Phys. Rev. E
99
(4
), 042118
(2019
).13.
G.
Jona-Lasinio
, “Thermodynamics of stationary states
,” J. Stat. Mech.: Theory Exp.
2014
(2
), P02004
.14.
T.
Speck
and U.
Seifert
, “Integral fluctuation theorem for the housekeeping heat
,” J. Phys. A: Math. Gen.
38
(34
), L581
(2005
).15.
D.
Mandal
and C.
Jarzynski
, “Analysis of slow transitions between nonequilibrium steady states
,” J. Stat. Mech.: Theory Exp.
2016
(6
), 063204
.16.
C.
Maes
and K.
Netočný
, “Nonequilibrium calorimetry
,” J. Stat. Mech.: Theory Exp.
2019
(11
), 114004
.17.
Y.
Zhang
, M.
Litniewski
, K.
Makuch
, P. J.
Żuk
, A.
Maciołek
, and R.
Hołyst
, “Continuous nonequilibrium transition driven by heat flow
,” Phys. Rev. E
104
, 024102
(2021
).18.
G.
Paul
and I.
Prigogine
, “On a general evolution criterion in macroscopic physics
,” Physica
30
(2
), 351
–374
(1964
).19.
C.
Maes
and K.
Netočnỳ
, “A nonequilibrium extension of the Clausius heat theorem
,” J. Stat. Phys.
154
(1
), 188
–203
(2014
).20.
D. P.
Ruelle
, “Extending the definition of entropy to nonequilibrium steady states
,” Proc. Natl. Acad. Sci. U. S. A.
100
(6
), 3054
–3058
(2003
).21.
S.-i.
Sasa
, “Possible extended forms of thermodynamic entropy
,” J. Stat. Mech.: Theory Exp.
2014
(1
), P01004
.22.
T. S.
Komatsu
and N.
Nakagawa
, “Expression for the stationary distribution in nonequilibrium steady states
,” Phys. Rev. Lett.
100
(3
), 030601
(2008
).23.
T. S.
Komatsu
, N.
Nakagawa
, S.-i.
Sasa
, and H.
Tasaki
, “Steady-state thermodynamics for heat conduction: Microscopic derivation
,” Phys. Rev. Lett.
100
(23
), 230602
(2008
).24.
T. S.
Komatsu
, N.
Nakagawa
, S.-i.
Sasa
, and H.
Tasaki
, “Entropy and nonlinear nonequilibrium thermodynamic relation for heat conducting steady states
,” J. Stat. Phys.
142
(1
), 127
–153
(2011
).25.
Y.
Chiba
and N.
Nakagawa
, “Numerical determination of entropy associated with excess heat in steady-state thermodynamics
,” Phys. Rev. E
94
(2
), 022115
(2016
).26.
N.
Nakagawa
and S.-i.
Sasa
, “Liquid-gas transitions in steady heat conduction
,” Phys. Rev. Lett.
119
(26
), 260602
(2017
).27.
N.
Nakagawa
and S.-i.
Sasa
, “Global thermodynamics for heat conduction systems
,” J. Stat. Phys.
177
(5
), 825
–888
(2019
).28.
S.-i.
Sasa
, N.
Nakagawa
, M.
Itami
, and Y.
Nakayama
, “Stochastic order parameter dynamics for phase coexistence in heat conduction
,” Phys. Rev. E
103
(6
), 062129
(2021
).29.
N.
Nakagawa
and S.-i.
Sasa
, “Unique extension of the maximum entropy principle to phase coexistence in heat conduction
,” Phys. Rev. Res.
4
(3
), 033155
(2022
).30.
S. R.
De Groot
and P.
Mazur
, Non-Equilibrium Thermodynamics
(Courier Corporation
, 2013
).31.
P. J.
Żuk
, K.
Makuch
, R.
Hołyst
, and A.
Maciołek
, “Transient dynamics in the outflow of energy from a system in a nonequilibrium stationary state
,” Phys. Rev. E
105
(5
), 054133
(2022
).32.
H. J.
Kreuzer
, Nonequilibrium Thermodynamics and Its Statistical Foundations
(Oxford University Press
, New York
, 1981
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
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