Temperature and correlations in 1-dimensional systems

Giberti, Claudio; Rondoni, Lamberto; Vernia, Cecilia

doi:10.1140/epjst/e2019-800138-8

Cited by 9 publications

(13 citation statements)

References 55 publications

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“…This expression bears a striking resemblance with that of j n defined in Equations (17) and (18). Notice that of the two terms inẋ n e n =ẋ n K n +ẋ n V n , in the r.h.s.…”

Section: The Local Energy Flux Redefining the Energy Densitymentioning

confidence: 51%

“…Notice that of the two terms inẋ n e n =ẋ n K n +ẋ n V n , in the r.h.s. of Equations (17) and (18), herė x n K n is replaced by a mean kinetic energy contribution by the two particles, 1 2ẋ n K n + 1 2ẋ n+1 k n+1 . Concurrently,ẋ n V n is replaced by a 'center of mass' type term, 1 2 (ẋ n +ẋ n+1 ) V n .…”

Section: The Local Energy Flux Redefining the Energy Densitymentioning

confidence: 99%

“…After the earlier studies on equilibrium thermodynamics, in relatively recent years they have been exploited in the field of nonequilibrium statistical mechanics. A typical field of study is that of nonequilibrium stationary states (NESS) [14][15][16][17][18], or eventually transient states [19,20], when a temperature gradient is present at the line's boundaries. The temperature is usually identified with the kinetic temperature, i.e., it is assumed to be proportional to the variance of the velocity.…”

Section: Introductionmentioning

confidence: 99%

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On the Definition of Energy Flux in One-Dimensional Chains of Particles

Gregorio

2019

Entropy

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We review two well-known definitions present in the literature, which are used to define the heat or energy flux in one dimensional chains. One definition equates the energy variation per particle to a discretized flux difference, which we here show it also corresponds to the flux of energy in the zero wavenumber limit in Fourier space, concurrently providing a general formula valid for all wavelengths. The other relies somewhat elaborately on a definition of the flux, which is a function of every coordinate in the line. We try to shed further light on their significance by introducing a novel integral operator, acting over movable boundaries represented by the neighboring particles’ positions, or some combinations thereof. By specializing to the case of chains with the particles’ order conserved, we show that the first definition corresponds to applying the differential continuity-equation operator after the application of the integral operator. Conversely, the second definition corresponds to applying the introduced integral operator to the energy flux. It is, therefore, an integral quantity and not a local quantity. More worryingly, it does not satisfy in any obvious way an equation of continuity. We show that in stationary states, the first definition is resilient to several formally legitimate modifications of the (models of) energy density distribution, while the second is not. On the other hand, it seems peculiar that this integral definition appears to capture a transport contribution, which may be called of convective nature, which is altogether missed by the former definition. In an attempt to connect the dots, we propose that the locally integrated flux divided by the inter-particle distance is a good measure of the energy flux. We show that the proposition can be explicitly constructed analytically by an ad hoc modification of the chosen model for the energy density.

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“…This expression bears a striking resemblance with that of j n defined in Equations (17) and (18). Notice that of the two terms inẋ n e n =ẋ n K n +ẋ n V n , in the r.h.s.…”

Section: The Local Energy Flux Redefining the Energy Densitymentioning

confidence: 51%

Section: The Local Energy Flux Redefining the Energy Densitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Definition of Energy Flux in One-Dimensional Chains of Particles

Gregorio

2019

Entropy

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“…Despite such efforts, the derivation of Fourier law from microscopic dynamics remains one of the major open problems of theoretical physics [3]. Recently, various works have suggested that heat conduction in 1D systems need to be more closely investigated [2,[4][5][6][7], in view of the many anomalies that characterise such systems. In fact, establishing meaningful relationships between microscopic and macroscopic properties, primarily requires accurate definitions of the relevant observables.…”

Section: Introductionmentioning

confidence: 99%

Heat flux in one-dimensional systems

2019

Self Cite

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Understanding heat transport in one-dimensional systems remains a major challenge in theoretical physics, both from the quantum as well as from the classical point of view. In fact, steady states of one-dimensional systems are commonly characterized by macroscopic inhomogeneities, and by long range correlations, as well as large fluctuations that are typically absent in standard threedimensional thermodynamic systems. These effects violate locality -material properties in the bulk may be strongly affected by the boundaries, leading to anomalous energy transport-and they make more problematic the interpretation of mechanical microscopic quantities in terms of thermodynamic observables. Here, we revisit the problem of heat conduction in chains of classical nonlinear oscillators, following a Lagrangian and an Eulerian approach. The Eulerian definition of the flux is composed of a convective and a conductive component. The former component tends to prevail at large temperatures where the system behavior is increasingly gas-like. Finally, we find that the convective component tends to be negative in the presence of a negative pressure.

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“…In [15], the authors investigated analytically and numerically the effect of local thermodynamic equilibrium (LTE), for one-dimensional chains of N oscillators. It has been concluded that the standard laws and quantities of macroscopic systems are not appropriate to understand the behavior of such systems.…”

mentioning

confidence: 99%