| Summary: | The review deals with a <i>novel approach</i> (MNEQT) to nonequilibrium thermodynamics (NEQT) that is based on the concept of internal equilibrium (IEQ) in an enlarged state space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="fraktur">S</mi><mi mathvariant="bold">Z</mi></msub></semantics></math></inline-formula> involving <i>internal variables as additional state variables</i>. The IEQ macrostates are unique in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="fraktur">S</mi><mi mathvariant="bold">Z</mi></msub></semantics></math></inline-formula> and have no memory just as EQ macrostates are in the EQ state space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="fraktur">S</mi><mi mathvariant="bold">X</mi></msub><mo>⊂</mo><msub><mi mathvariant="fraktur">S</mi><mi mathvariant="bold">Z</mi></msub></mrow></semantics></math></inline-formula>. The approach provides a clear strategy to identify the internal variables for any model through several examples. The MNEQT deals directly with system-intrinsic quantities, which are very useful as they fully describe irreversibility. Because of this, MNEQT solves a long-standing problem in NEQT of identifying a unique global temperature <i>T</i> of a system, <i>thus fulfilling Planck’s dream of a global temperature for any system</i>, even if it is not uniform such as when it is driven between two heat baths; <i>T</i> has the conventional interpretation of satisfying the Clausius statement that the <i>exchange macroheat</i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>d</mi><mi mathvariant="normal">e</mi></msub><mi>Q</mi></mrow></semantics></math></inline-formula><i>flows from hot to cold</i>, and other sensible criteria expected of a temperature. The concept of the generalized macroheat <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mi>Q</mi><mo>=</mo><msub><mi>d</mi><mi mathvariant="normal">e</mi></msub><mi>Q</mi><mo>+</mo><msub><mi>d</mi><mi mathvariant="normal">i</mi></msub><mi>Q</mi></mrow></semantics></math></inline-formula> converts the Clausius inequality <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mi>S</mi><mo>≥</mo><msub><mi>d</mi><mi mathvariant="normal">e</mi></msub><mi>Q</mi><mo>/</mo><msub><mi>T</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula> for a system in a medium at temperature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>0</mn></msub></semantics></math></inline-formula> into the <i>Clausius equality</i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mi>S</mi><mo>≡</mo><mi>d</mi><mi>Q</mi><mo>/</mo><mi>T</mi></mrow></semantics></math></inline-formula>, which also covers macrostates with memory, and follows from the extensivity property. The equality also holds for a NEQ isolated system. The novel approach is extremely useful as it also works when no internal state variables are used to study nonunique macrostates in the EQ state space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="fraktur">S</mi><mi mathvariant="bold">X</mi></msub></semantics></math></inline-formula> at the expense of explicit time dependence in the entropy that gives rise to memory effects. To show the usefulness of the novel approach, we give several examples such as irreversible Carnot cycle, friction and Brownian motion, the free expansion, etc.
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