Laws
of Thermodynamics |

**In General, and Zeroth Law**

* __Zeroth law__: Two thermodynamical
systems which are both in equilibrium with a third one are also in equilibrium with each other.

@ __General references__: Abou Salem & Fröhlich JSP(07)mp/06 [status
of laws]; Atkins 10 [short introduction]; > s.a. thermodynamics; generalized thermodynamics [emergence of laws from quantum theory, extension to nanoscale systems].

@ __Zeroth law__:
Ramírez-Hernández et al PRL(08)
[with negative specific heat]; Gaveau & Schulman JSP(11)-a1108 [violations, for a non-ergodic interaction]; Haggard & Rovelli PRD(13)-a1302, IJMPD(13) [in relativistic theory]; Anza & Vedral sRep(17)-a1509 [information-theoretic version].

> __Online resources__: see Wikipedia page.

**First Law**

* __Idea__: In any thermodynamic process, the change in
internal energy of a system, the heat absorbed and the work done
are related by Δ*U* = *Q* – *W*.

* __Heat absorbed__: In an infinitesimal reversible transformation the
term d*Q* can be written as *mc*(*T*) d*T*, where *m* is
the mass and *c* the specific heat (at constant volume), or *T*d*S*,
depending on which variables are used; > s.a. heat [including engines].

* __Work done__: It can
have contributions from different processes; For example, in an infinitesimal reversible transformation d*W* = *p* d*V* + *t* d*A* + *f* d*L* – *μ* d*N* +
Φ d*Q + *(see black-hole laws) + ...;
Here, *p* is the pressure, *t* surface tension, *f* tension, *μ* chemical potential.

* __Fundamental identity__: d*U* is
a sum of products of conjugate quantities, *Intensive* · d(*Extensive*);
> s.a. thermodynamics.

@ __References__: Kapoulitsas PS(03)
[new formulation]; Martinez et al PhyA(05),
Plastino et al PhyA(06)
[from information theory].

> __Online resources__: see Wikipedia page.

**Second Law** > s.a. energy
conditions [violations]; entropy; *H* Theorem;
Maxwell's Demon; thermodynamic systems; Szilard's Demon.

$ __Kelvin formulation__: Not all heat can be converted into work with no other change
in the system or surroundings.

$ __Clausius formulation__: No cyclic engine can just transfer thermal energy from a
colder body to a hotter one.

$ __Minimal work principle__:
One of the formulations of the second law, states that work done on a thermally
isolated equilibrium system is minimal for adiabatically slow (reversible) realization
of a given process.

* __Remark__: The second law is not synonymous
with inescapable collapse into disorder, but allows self-organization.

* __Remark__: It has been said by Sir Arthur Eddington to hold the "supreme position among the laws of Nature".

@ __General references__: Marcella AJP(92)oct
[and entropy]; Bennett SA(87)nov [demons]; Atkins 94 [I]; Berger PE(94)ao/95 [interpretation];
Allahverdyan & Nieuwenhuizen PRE(05)cm/04 [minimal
work]; Maes & Tasaki LMP(07)
[macroscopic system + microscopic degrees of freedom]; Sheehan FP(07)
[foundations and status]; Lemos & Penner AJP(08)jan
[Sadi Carnot]; Campisi SHPMP(08)
[proof based on volume entropy]; Davey PhSc(08)jan
[re justification based on probability]; Kaila & Annila PRS(08);
Van Willigenburg & De Koning FP(09)
[and reversible dynamics]; Mello & Rodríguez EJP(13) [thermally but not mechanically isolated systems]; Hari Dass a1306 [the first part implies the second part]; Narnhofer & Wreszinski PRP(14)-a1309, Tasaki PRL(16)-a1511 [quantum version].

@ __And information theory__: Zhang
IJMPE(08)qp/06;
Duncan & Semura FP(07); news nat(10)nov [converting information into work]; Parker PhSc(11) [Jaynes' proof]; Deffner & Jarzynski PRX(13) [fundamental framework]; Bartolotta et al PRE(16)-a1508 [Bayesian].

@ __Other views, generalizations__: Lieb & Yngvason
PRP(99),
PT(00)mp,
in(02)mp;
Davies & Davis FP(02)ap/03 [with
black holes]; Gyftopoulos & Beretta qp/05; Hasegawa et al PLA(10)
[for a non-equilibrium initial state]; Bokhari & Akbar IJMPD(10)
[generalized, in wormhole geometry]; Tegmark PRD(12)-a1108 [generalized tripartite framework, and unitary cosmology]; Myrvold SHPMP(11) [Maxwell's view]; Aurell et al JSP(12) [refined version for fast random processes]; Egloff et al NJP(15)-a1207 [beyond the von Neumann regime]; Bousso & Engelhardt PRD(16)-a1510 [in cosmology, outside past Q-screens]; Richens et al a1702 [finite-bath corrections]; > s.a. black-hole
thermodynamics; networks.

@ __On violations__: PW(90)dec [perpetual motion];
Wang et al PRL(02)
[short time, mesoscopic]; Minkel SA(03)jun [quantum]; Ford & O'Connell PRL(06)qp [quantum,
and resolution]; Gyftopoulos & von Spakovsky a0706, a0706,
Gyftopoulos a0706 [no
nanoscale violations]; Rubí SA(08)nov [order
from chaos]; Saha et al PRE(09)
[entropy production fluctuations]; Bandyopadhyay PS(10) [quantum,
and resolution]; news pw(13)apr [spin waves carry energy from cold to hot]; Argentieri et al EPL(14)-a1408 [non-completely-positive dynamics]; > s.a. condensed matter [small scales]; Perpetuum
Mobile.

@ __At the microscopic scale__: Feng EJTP(04)qp/05 [microscopic
origin]; Josset FP(17)-a1702.

@ __Related topics__: Uffink SHPMP(01)
[and arrow of time]; Allahverdyan & Nieuwenhuizen PhyA(02)cm/01 [basis];
Martín-Olalla & Rey de Luna JPA(03)
[and Nernst theorem]; Forrester a0811 [entropy
and growth of knowledge]; > s.a. quantum measurement.

> __Online resources__: see Wikipedia page.

**Third Law** > s.a. black-hole thermodynamics;
brownian motion; Free
Energy; quantum phase transitions; temperature [minimum value].

* __Idea__:
As *T* → 0, the heat capacity of a thermodynamical system goes
to zero; In the Nernst formulation, as *T* → 0, *S* → 0
or a constant, independent of all parameters of the system.

@ __References__: Lavenda & Gunning-Davies NCB(95);
Blau & Halfpap AJP(96)jan-Q;
Dimitrov qp/97;
Wald
PRD(97)gq [black
holes
and limitations]; Belgiorno JPA(03), JPA(03);
O'Connell JSP(06)qp [quantum
regime]; Wreszinski & Abdalla JSP(09)-a0710 [precise
formulation and applications]; Kolář et al PRL(12)-a1208 [challenge to the Nernst formulation]; Masanes & Oppenheim a1412 [derivation].

> __Online resources__: see Wikipedia page.

**Related Topics** > see laws of black-hole
thermodynamics [fourth law].

‘In this house, young lady, we OBEY the laws of thermodynamics’

Homer
Simpson punishing Lisa for making a perpetual motion machine

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