Nonequilibrium Temperature: An Approach from Irreversibility

Lucia, Umberto; Grisolia, Giulia

doi:10.3390/ma14082004

Cited by 8 publications

(5 citation statements)

References 68 publications

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“…It is not possible to list all of them here. So, we have selected a few of these attempts [13,18,23,[226][227][228][229][230][231][232] to show how our approach is different from all of them, without casting any aspersions on those that are omitted. Our thermodynamic definition in Equation (1) refers to the entire body, so it is not local.…”

Section: Brief Discussion and Summarymentioning

confidence: 99%

Foundations of Nonequilibrium Statistical Mechanics in Extended State Space

Gujrati

2023

Foundations

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The review provides a pedagogical but comprehensive introduction to the foundations of a recently proposed statistical mechanics (μNEQT) of a stable nonequilibrium thermodynamic body, which may be either isolated or interacting. It is an extension of the well-established equilibrium statistical mechanics by considering microstates mk in an extended state space in which macrostates (obtained by ensemble averaging A^) are uniquely specified so they share many properties of stable equilibrium macrostates. The extension requires an appropriate extended state space, three distinct infinitessimals dα=(d,de,di) operating on various quantities q during a process, and the concept of reduction. The mechanical process quantities (no stochasticity) like macrowork are given by A^dαq, but the stochastic quantities C^αq like macroheat emerge from the commutator C^α of dα and A^. Under the very common assumptions of quasi-additivity and quasi-independence, exchange microquantities deqk such as exchange microwork and microheat become nonfluctuating over mk as will be explained, a fact that does not seem to have been appreciated so far in diverse branches of modern statistical thermodynamics (fluctuation theorems, quantum thermodynamics, stochastic thermodynamics, etc.) that all use exchange quantities. In contrast, dqk and diqk are always fluctuating. There is no analog of the first law for a microstate as the latter is a purely mechanical construct. The second law emerges as a consequence of the stability of the system, and cannot be violated unless stability is abandoned. There is also an important thermodynamic identity diQ≡diW≥0 with important physical implications as it generalizes the well-known result of Count Rumford and the Gouy-Stodola theorem of classical thermodynamics. The μNEQT has far-reaching consequences with new results, and presents a new understanding of thermodynamics even of an isolated system at the microstate level, which has been an unsolved problem. We end the review by applying it to three different problems of fundamental interest.

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Section: Brief Discussion and Summarymentioning

confidence: 99%

Foundations of Nonequilibrium Statistical Mechanics in Extended State Space

Gujrati

2023

Foundations

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“…To let time go [ 31 , 32 , 33 , 34 ] and replace its function by a causality principle is a difficult task apparently, but to the authors it is a much easier task than to let go of causality. However, further elaborations on the concept of causality both at the mathematical [ 35 , 36 ] and physical level [ 1 , 23 , 37 ] and the link to the macroscopic arrow of time [ 18 , 38 , 39 , 40 , 41 , 42 ] are indicated to be key for a further development of fundamental physical theories. With the introduction of causality introduced here, time can only be reconstructed as a discrete entity also yielding other consequences from entropy [ 16 , 18 , 38 ] to the evolution of the universe [ 43 ] and many other findings [ 44 , 45 , 46 , 47 , 48 ], and thus opening more avenues to be studied.…”

Section: Discussionmentioning

confidence: 99%

Causality in Discrete Time Physics Derived from Maupertuis Reduced Action Principle

Riek

Chatterjee

2021

Entropy

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Causality describes the process and consequences from an action: a cause has an effect. Causality is preserved in classical physics as well as in special and general theories of relativity. Surprisingly, causality as a relationship between the cause and its effect is in neither of these theories considered a law or a principle. Its existence in physics has even been challenged by prominent opponents in part due to the time symmetric nature of the physical laws. With the use of the reduced action and the least action principle of Maupertuis along with a discrete dynamical time physics yielding an arrow of time, causality is defined as the partial spatial derivative of the reduced action and as such is position- and momentum-dependent and requests the presence of space. With this definition the system evolves from one step to the next without the need of time, while (discrete) time can be reconstructed.

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“…Note that we have used the identity ∑ k dp k = 0 above; see also Equation (108). We introduce a special process, to be called a generalized isometric process, which is a process at fixed W(t) and is a generalization of an isochoric process.…”

Section: Statistical Significance Of Dw and Dqmentioning

confidence: 99%

“…There is a recent attempt [ 108 ] to introduce another NEQ temperature by using fluctuation theorems to determine the entropy generation, which is then related to the Gouy-Stodola theorem derived later (see Equation ( 84b )). It is limited to a interacting

in a medium

so does not apply to an isolated system.…”

Section: Unique Macrostatesmentioning

confidence: 99%

A Review of the System-Intrinsic Nonequilibrium Thermodynamics in Extended Space (MNEQT) with Applications

Gujrati

2021

Entropy

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The review deals with a novel approach (MNEQT) to nonequilibrium thermodynamics (NEQT) that is based on the concept of internal equilibrium (IEQ) in an enlarged state space SZ involving internal variables as additional state variables. The IEQ macrostates are unique in SZ and have no memory just as EQ macrostates are in the EQ state space SX⊂SZ. 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 T of a system, thus fulfilling Planck’s dream of a global temperature for any system, even if it is not uniform such as when it is driven between two heat baths; T has the conventional interpretation of satisfying the Clausius statement that the exchange macroheatdeQflows from hot to cold, and other sensible criteria expected of a temperature. The concept of the generalized macroheat dQ=deQ+diQ converts the Clausius inequality dS≥deQ/T0 for a system in a medium at temperature T0 into the Clausius equalitydS≡dQ/T, 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 SX 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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Nonequilibrium Temperature: An Approach from Irreversibility

Cited by 8 publications

References 68 publications

Foundations of Nonequilibrium Statistical Mechanics in Extended State Space

Foundations of Nonequilibrium Statistical Mechanics in Extended State Space

Causality in Discrete Time Physics Derived from Maupertuis Reduced Action Principle

A Review of the System-Intrinsic Nonequilibrium Thermodynamics in Extended Space (MNEQT) with Applications

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