Microcanonical entropy: consistency and adiabatic invariance

Tavassoli, Arash; Montakhab, Afshin

doi:10.48550/arxiv.1512.02855

Cited by 3 publications

(6 citation statements)

References 31 publications

(68 reference statements)

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“…i dE (i) = 0. Note that for n = 2 subsystems, this becomes dE (II) = −dE (I) = δE (II,I) and the drift force is proportional to the difference of its inverse temperatures dF , = (1/T (II) − 1/T (I) )δE (II,I) , ( 6 ) with δE (II,I) as the amount of energy transfer from system I to II. Hence dF , directs heat flow towards the colder subsystem, i.e.…”

Section: Thermodynamic Driving Forces and Boltzmann Entropymentioning

confidence: 99%

“…It must be stressed here that for the above derivations no presuppositions about the inner structure of the subsystems were made. In particular this means that equations ( 5) and (6) are not restricted to extensive subsystems, which fulfill the thermodynamic limit. Instead any subsystem is conceivable, in particular subsystems which consist of strongly interacting elements as the GFSs.…”

Section: Thermodynamic Driving Forces and Boltzmann Entropymentioning

confidence: 99%

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How geometrically frustrated systems challenge our notion of thermodynamics

Bauer¹

2022

J. Stat. Mech.

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Although Boltzmann’s definition of entropy and temperature are widely accepted, we will show scenarios which apparently are inconsistent with our normal notion of thermodynamics. We focus on generic geometrically frustrated systems (GFSs), which stay at constant negative Boltzmann temperatures, independent from their energetic state. Two weakly coupled GFSs at same temperature exhibit, in accordance with energy conservation, the same probability for all energetic combinations. Heat flow from a hot GFS to a cooler GFS or an ideal gas increases Boltzmann entropy of the combined system, however the maximum is non-local, which, in contrast to conventional thermodynamics, implies that both subsystems maintain different temperatures here. Re-parametrization can transform these non-local into local maxima with corresponding equivalence of re-defined temperatures. However, these temperatures cannot be assigned solely to a subsystem but describe combinations of both. The non-local maxima of entropy restrict the naive application of the zeroth law of thermodynamics. Reformulated this law is still valid with the consequence that a GFS at constant negative temperature can measure positive temperatures. Heat exchange between a GFS and a polarized paramagnetic spin gas, i.e. a system that may achieve besides positive also negative temperatures, drives the combined system to a local-, or non-local maximum of entropy, with equivalent or non-equivalent temperatures here. Energetic constraints determine which scenario results. In case of a local maximum, the spin gas can measure temperature of the GFS like a usual thermometer, however, this reveals no information about the energetic state of the GFS.

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Section: Thermodynamic Driving Forces and Boltzmann Entropymentioning

confidence: 99%

Section: Thermodynamic Driving Forces and Boltzmann Entropymentioning

confidence: 99%

How geometrically frustrated systems challenge our notion of thermodynamics

Bauer¹

2022

J. Stat. Mech.

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“…radiofrequency pulses, turning the spins. Whether Gibbs entropy is applicable to particle exchange and the chemical potential is also matter of debate [8]. This is most probably related to the fact that Gibbs entropy and derived quantities treat energy and particles in a non-symmetric way.…”

Section: A Boltzmann Temperature and Drift Forcesmentioning

confidence: 99%

“…One main argument in favor of Gibbs entropy is that it is consistent with the adiabatic invariance of phase space volume [6,7] and in revealing the same thermodynamic forces as statistical mechanics does. Others claim that this statement is not always applicable, in particular to the chemical potential [8]. A further argument against Gibbs entropy is that its limitation to describe combined systems, which are paradigms of thermodynamics, e.g.…”

Section: Introductionmentioning

confidence: 99%

How Geometrical Frustrated Systems Challenge our Notion of Thermodynamics

Bauer

2021

Preprint

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Although Boltzmann's definition of entropy, and, hence, the existence of negative temperatures, are widely accepted, we will show scenarios which apparently at a first glance are inconsistent with our normal notion of thermodynamics. This is shown in the framework of stochastic thermodynamics for special geometrical frustrated systems (GFSs), which have maximum entropy at its ground state and constant negative temperature. For two GFSs in weak thermal contact and at same temperature, all energetic constellations are equal probable. A hot and a cool GFS in contact is driven by entropic forces via heat transfer to a most probable state in which the hot GFS is in its ground state. The same holds for a GFS in contact with a gas. As this is not a local maximum of entropy both subsystems maintain different temperatures here. Re-parametrization can transform these non-local into local maxima with corresponding equivalence of re-defined temperatures. However, these temperatures cannot be assigned solely to a subsystem but describe combinations of both.The non-local maxima of entropy restrict the naive application of the zeroth law of thermodynamics. Reformulated this law is still valid with the consequence that a GFS at constant negative temperature can measure positive temperatures. A GFS combined with a polarized paramagnetic spin gas may have a local or non-local maxima of entropy, with equivalent or non-equivalent temperatures, respectively. In case of a local maximum the spin gas can measure the temperature of the GFS, however, it does not reveal information about its energetic state.

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“…Therefore, one can see that the consistency relation holds only if one can move in the differentiation into the integration on state space, i. e. trace operation. This is clearly not allowed and has in fact been proved to be false in specific and explicit cases 2 . If one replaced Tr with ... d 3N pd 3N q/h 3N for a classical system, the lack of interchangeability will become more evident.…”

mentioning

confidence: 99%