Entropy |

**In General** > s.a. chaos;
MaxEnt (Maximum Entropy Principle); history
of physics; statistical mechanics; thermodynamics.

* __Thermodynamic entropy__:
An extensive thermodynamical function of state which is non-decreasing for
adiabatic transformations (constant in reversible ones); In most systems,
it grows monotonically with *E*; The concept was introduced by
Clausius in the 1860s and the Clausius entropy is defined, up to an
additive constant, by the relation d*S* = d*Q*/*T*.

* __Statistical
interpretation__: A measure of how spread out a classical distribution
function or quantum density *ρ* matrix is; It can be defined in
various ways; For a quantum density matrix *ρ*, the von Neumann
entropy is defined by *S* = −*k*_{B}
tr *ρ* ln *ρ*; > s.a. types
of entropies.

* __And classical /
quantum mechanics__: In classical mechanics one assumes entropies are
finite, but if one takes the \(\hbar\) → 0 limit of any quantum entropy
expression, this diverges; So classical thermodynamics is not the classical
limit of quantum statistical mechanics, it knows about quantum mechanics.

@ __Articles, II__: Han et al cm/97,
AJP(99)jan [tracing over degrees of freedom];
Styer AJP(00)dec [examples and meaning];
Lieb & Yngvason PT(00)apr [without thermodynamics];
Styer AJP(08)oct [and evolution];
Salagaram & Chetty AJP(11)nov [computation].

@ __Books__: Martin & England 81;
Denbigh & Denbigh 85;
Leff & Rex ed-90;
Dugdale 96 [II];
Scully & Scully 07
[Maxwell's demon, information, and the quantum];
Grandy 08 [and probability];
Ben-Naim 16 [I].

@ __General references__:
Wehrl RMP(78);
in Sorkin PRL(86);
Mackey RMP(89) [increasing entropy and ergodicity];
Lavenda et al NCB(95);
Leff AJP(96)oct [and energy sharing];
Levy math/06 [mathematical interpretation];
Kozlov & Treshchev TMP(07) [coarse-grained];
Bernstein a1109 [pedagogical];
Baumgartner FP(14)-a1206 [axiomatic characterization and derived facts];
Zanchini & Beretta Ent(14)-a1403 [general definition];
Phillips TPT(16) [entropy as the spread of energy];
Jakšić a1806 [and information theory].

@ __Conceptual__: Leff FP(07) [language and interpretation];
Topsoe a0807 [entropy and truth vs belief];
Timberlake TPT(10) [statistical interpretation];
Swendsen AJP(11)apr [definitions and meaning];
Baez et al Ent(11)-a1106 [characterization in terms of information loss];
Davey PhSc(11) [and probability];
Swendsen FP(12) [argument for probabilistic definition];
Dieks a1209-in [thermodynamical vs statistical-mechanical definitions];
Benguigui EJP(13)-a1209 [different definitions];
Caticha M&M-a1412
[entropic inference as a general framework for reasoning under conditions of uncertainty];
in Oltean et al PRD(16)-a1607 [nature of *S*];
Toffoli Ent(16)-a1705 [and "honest entropy"].

@ __And observation__: Steane NJP(16)-a1510 [determining absolute entropy without quantum theory or the third law].

**Related Concepts and Generalizations**
> s.a. Coarse Graining; Disentropy;
dissipation; Entropic Dynamics;
Homogeneity.

@ __And area law__:
Mäkelä gq/06-GRF;
Masanes PRA(09)-a0907 [for low-energy states].

@ __Other properties__: Kay & Kay JPA(01)mp/98 [strong subadditivity and volume];
Touchette AJP(08)jan [(non)-concavity].

@ __Subsystems__: Hotta & Joichi PLA(99)cm [additivity];
Baumgartner JPA(02)mp/01;
Dupuis et al a1607 [additivity, "accumulation"].

@ __Entropy current__: Bhattacharyya JHEP(14)-a1403,
JHEP(14) [and the equilibrium partition function];
Banerjee et al JHEP(14) [non-relativistic fluid].

@ __Beyond equilibrium situations__: Beretta & Zanchini in(11)-a1010;
Beretta & Zanchini a1411 [and few-particle systems];
> s.a. non-equilibrium thermodynamics.

@ __And time__: Hotke-Page & Page in(92) [clock time];
Ben-Naim 16 [no relationship].

@ __Entropy production and arrow of time__:
Parrondo et al NJP(09);
Martyushev & Shaiapin Ent(16)-a1605.

@ __Related topics__: Hall PRA(99)qp/98 [geometric, ensemble volume];
Leff AJP(99)dec [dimensionless];
Dover PhyA(04) [and scaling laws];
Hanel et al PNAS(12)-a1211 [generalized, for systems violating the Shannon-Khinchin axioms];
Lieb & Yngvason PRS(14)-a1403 [entropy meters and the entropy of non-extensive systems];
Plastino et al PhyA(14)
[partition function and entropy from thermodynamics];
Chafaï AFST(15)-a1405 [aspects of entropy in different disciplines].

__Related topics__:
see entropy bounds; entropy in quantum theory;
types of entropies and entanglement entropy.

**Systems**

> __Gravity-related__:
see black-hole entropy; gravitational
thermodynamics; horizons.

> __Other systems__:
see casimir effect [negative entropies];
cell complex; cellular
automaton; networks; thermodynamic
systems; tilings.

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