Laws of Thermodynamics  

In General, and Zeroth Law > s.a. complexity.
* The "minus first law": In the absence of external interventions, a thermodynamic system will equilibrate in a finite time and then remain in equilibrium.
* 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 ΔU = QW.
* Heat absorbed: In an infinitesimal reversible transformation the term dQ can be written as mc(T) dT, where m is the mass and c the specific heat (at constant volume), or TdS, 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 dW = p dV + t dA + f dLμ dN + Φ dQ + (see black-hole laws) + ...; Here, p is the pressure, t surface tension, f tension, μ chemical potential.
* Fundamental identity: dU 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]; Wu a2010 [deductive 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]; Lutz & Ciliberto PT(15)sep [rev]; 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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