Thermodynamics |

**In General**
> s.a. Kinetic Theory; quantum field theory;
statistical mechanics; thermodynamic systems.

* __Idea__: The study of the possible
internal states of macroscopic systems; It uses macroscopic variables such as
*n* or *N*, *p*, *V*, *T*, *S*, and the
chemical potential *μ*, related by equations of state, as the basic ones.

* __Motivation__: Originally, it was important
because of engineering applications (for example, heat \(\mapsto\) work in locomotives
or work \(\mapsto\) heat in cannon boring and Joule's experiments; Now it is important
because it involves the relationship between macroscopic and microscopic descriptions,
information, and time.

**Formalism and Effects** > s.a. coherent states; laws
of thermodynamics; heat [including bath]; Heat Engines;
Legendre Transform; time.

* __Fundamental identity__:
An expression for d*U* as a sum of products of conjugate quantities,
for example d*U = T* d*S* − *p* d*V*;
Not to be confused with the first law of thermodynamics, d*U*
= d*Q* − d*W*.

* __Geometry of state space__:
Different metrics that have been introduced are the Ruppeiner metric, Weinhold metric, and Quevedo metric.

@ __General references__: Lavenda 95 [extreme situations];
Cooper a1108 [systematic approach to thermodynamical identities];
Etkin a1401 [methodological principles];
Sewell RPMP(19)-a1808 [quantum statistical
basis for a complete set of thermodynamic variables and differentiability of entropy].

@ __Coarse-graining__:
Schulman & Gaveau FP(01) [scale, and order];
> s.a. entropy; lattice field theory.

@ __Phase separation__: Gross PhyE(05)cm/04-in [and microcanonical statistics].

@ __Geometry of state space__: Chen JMP(99);
Santoro & Preston mp/05 [2 degrees of freedom, Weinhold metric];
Quevedo JMP(07)phy/06;
Quevedo et al a0811 [ideal gas];
Pavlov & Sergeev TMP(08) [symplectic structure and Hamiltonian];
Vázquez et al JGP(10)-a1101;
Quevedo et al GRG(11)-a1010 [phase transitions];
Ruppeiner AJP(10)nov,
Quevedo et al JKPS(10)-a1011 [thermodynamic curvature and interactions];
Cooper & Russell a1102 [state space as a measure space with two orderings];
Quevedo & Ramírez a1205 [van der Waals system, phase transition];
Sivak & Crooks PRL(12) [from friction tensor];
Bravetti & Nettel PRD(14)-a1208 [thermodynamic curvature];
Mansoori et al JHEP(11)-a1411;
Mansoori et al PLB(16)-a1602 [extrinsic curvature];
Kocik a1807-in;
Mansoori & Mirza PLB-a1905 [new thermodynamic geometry];
> s.a. black-hole thermodynamics;
Geometrothermodynamics; phase transitions;
Ruppeiner Metric; thermodynamic systems.

@ __Lagrangian description__: Vaz a1110 [motivated by possible microstructure of spacetime].

@ __Hamiltonian approach__:
Maslov TMP(94) [and quantization];
Baldiotti et al AP(16)-a1604.

@ __And information theory__: Gagliardi & Di Carlo PhyA(12) [information-related potentials];
Strasberg et al PRX(17)-a1610 [framework];
Bera et al Quant(19)-a1707 [thermodynamics from information conservation];
Faist & Renner PRX(18) [work cost of quantum processes];
Deffner & Campbell a1907-book [quantum];
> s.a. information and physics; thermodynamic laws.

@ __Related topics__: Ghosh & Mukhopadhyay AJP(95)aug [and macroscopic motion];
Hannay AJP(06)feb [Carnot's vector field formulation];
Kerr & Macosko AJP(11)sep [Venn diagrams for potentials].

@ __Reversible processes__: Samiullah AJP(07)jul;
Norton SHPMP(16) [the notion is self-contradictory].

> __Basic concepts__: see Chemical Potential;
energy [equipartition]; Enthalpy; Equation
of State; Free Energy; heat;
temperature; Thermodynamic Limit.

> __Other concepts__: see Compressibility;
Contact Geometry; entanglement;
Exergy; Extensive Quantities;
specific heat; Phase Diagram;
vacuum.

> __Effects, phenomena__:
see Continuous Media; critical phenomena;
Elasticity; Joule Expansion;
Paradoxes; phase transitions;
Thermoluminescence.

> __Results__: see Gibbs-Duhem Relation;
hamilton-jacobi theory; Initial Conditions;
Maxwell Relations.

> __Generalized frameworks__: see modified
thermodynamics; non-equilibrium thermodynamics;
non-extensive statistical mechanics.

**References**
> s.a. computation and computational physics;
generalized; history; physics
teaching; statistical mechanics.

@ __Books, I__: Goldstein 93;
Schneider & Sagan 05 [and life];
Atkins 07.

@ __Books, II__: Bergmann 62;
Morse 64;
Kittel & Kroemer 80 [statistical mechanics first];
Berry 91;
Bailyn 94 [historical];
Carrington 94;
Lee 02 [entropy, free energy];
Turns 06;
Stowe 07;
Lemons 08;
Blundell & Blundell 09 [r PT(07)oct];
Helrich 09 [and irreversibility];
Gould & Tobochnik 10
[+ programs];
Hoch 11;
Goodstein 15;
Olla 15;
Tosun 15;
Reynolds & Colonna 18 [engineering];
Ansermet & Brechet 19 [not stat mech].

@ __Books, III__:
O'Connell & Haile 05 [chemical engineering];
Cheng 06 [statistical];
Honig 07;
de Oliveira 13;
Hari Dass 13;
Daily 18 [engineering].

@ __Books, problems__: Lim 90.

@ __Books__: Bridgman 41 [conceptual];
Fermi 57;
Pippard 64;
Schrödinger 64;
Truesdell 84;
Callen 85;
Griffiths 85;
Guggenheim 85;
Waldram 85;
Martin 86;
Bauman 92;
Greiner et al 95;
Zemansky & Dittman 97;
Assael et al 11 [commonly asked questions].

@ __Conceptual foundations__: Emch & Liu 02 [logic];
Callender SHPMP(01) [re taking thermodynamics too literally];
Hemmo & Shenker SHPMP(01),
PhSc(03)apr,
SHPMP(05) [from decoherence?];
Antoniou FP(02) [Carathéodory];
Mahler et al PhyE(05)qp [in composite systems];
Abou Salem & Fröhlich JSP(07)mp/06 [status of laws];
Myrvold a2007 [fundamental physics vs manipulations];
> s.a. statistical mechanics [approach to equilibrium];
Thermodynamic Limit.

@ __Mathematical foundations__: Giles 64;
Owen 84;
Sewell RPMP(13) [formulations of local thermodynamical equilibrium conditions, three levels];
Wreszinski a2003 ["one or two small points"].

> __Online resources__: Internet Encyclopedia of Science
pages.

"Every mathematician knows it is impossible to understand
an elementary course in thermodynamics." Vladimir I Arnold;

"If someone points out to you that your pet theory of the universe is in
disagreement with Maxwell's equations—then so much the worse for Maxwell's equations.
If it is found to be contradicted by observation—well these experimentalists do bungle
things sometimes. But if your theory is found to be against the second law of thermodynamics
I can give you no hope; there is nothing for it but to collapse in deepest humiliation."

Sir Arthur Stanley Eddington, Gifford Lectures (1927), The Nature of the Physical World (1928).

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