Laws of Thermodynamics |

**In General, and Zeroth Law** > s.a. complexity.

* __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.

@ __Generalizations__:
Bera et al nComm(17)-a1612 [with correlations];
> s.a. generalized thermodynamics [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];
Anza & Vedral sRep(17)-a1509 [information-theoretic version];
Kammerlander & Renner a1804
[as a consequence of the first and the second laws].

@ __Zeroth law, relativistic__: Haggard & Rovelli PRD(13)-a1302,
IJMPD(13);
Gavassino a2005 [manifestly covariant].

> __Online resources__:
see Wikipedia page.

**First Law** > s.a. quantum thermodynamics.

* __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; quantum thermodynamics;
thermodynamic systems.

$ __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.

$ __Planck formulation__: In any
naturally occurring process the sum of the entropies of all bodies taking part
in the process is increased.

$ __Minimal work formulation__: The
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];
news sn(10)jun [extracting work from random motion];
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];
Wreszinski a1902 [dynamical proof];
> s.a. non-equilibrium systems.

@ __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 PRE(18)-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];
Josephson Effect [backwards heat flow];
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. Landauer's Erasure Principle; quantum
measurement; Szilard's Demon.

> __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; As unattainability principle,
the impossibility of bringing a system to its ground state in a finite time.

@ __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 nComm(17)-a1412 [derivation];
Wilming & Gallego PRX(17)-a1701;
Kieu PLA(19)-a1804 [vs the Principle of Unattainability];
Freitas et al in(18)-a1911 [derivations of the unattainability principle];
Marquet a1904,
a1904 [why it is relevant].

> __Online resources__:
see Wikipedia page.

**Related Topics**

@ __Fourth law__: Beretta PTRS-a1908-conf [steepest entropy ascent];
> s.a. laws of black-hole thermodynamics.

"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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