Abstract
Local thermodynamic equilibrium (LTE) plays a crucial role in statistical mechanics and thermodynamics. Under small driving and LTE, locally conserved quantities are transported as prescribed by linear hydrodynamic laws, in which the local material properties of the systems at hand are represented by the transport coefficients. The robustness and universality of equilibrium properties is not guaranteed in nonequilibrium states, in which different microscopic quantities may behave differently, even if they coincide at equilibrium. We investigate these issues considering 1-dimensional chains of N oscillators. We observe that non-negligible fluctuations, and persistence of correlations frustrate the onset of LTE, hence the existence of thermodynamic fields, such as temperature.
Highlights
In their seminal paper Ref.[1], Rieder, Lebowitz and Lieb investigated the properties of 1dimensional systems made of N harmonic oscillators, with only nearest neighbors and, at their ends, with stochastic heat baths
Fluctuations, in particular, are characteristic of particles systems: they are larger in size for larger systems, and they may be observed in macroscopic systems [11, 12], but they must be negligible on the scale of observation, for the thermodynamic laws to hold
The hard-core nature of the Lennard-Jones potential (LJ) potentials preserves the order of particles: 0 < x1 < x2 < · · · < xN < (N + 1)a holds at all times, if it does at the initial time [42]
Summary
In their seminal paper Ref.[1], Rieder, Lebowitz and Lieb investigated the properties of 1dimensional systems made of N harmonic oscillators, with only nearest neighbors and, at their ends, with stochastic heat baths. The fact is that the amounts corresponding to macroscopic observations are minimal compared to those stored at the the microscopic levels When this is the case, thermodynamic laws may apply, and conduction, associated with disordered motions, can be distinguished from convection, which is associated with regular motion, capable of doing mechanical work. Analogous considerations hold for the definition of heat flux, that requires a clear distinction between energy transport due to macroscopic motions (convection), and transport without macroscopic motions (conduction), cf Chapter 4 of Ref.[35], and Section III. and Chapter XI of Ref.[36] To clarify these issues, we compare single particle with local mesoscopic quantities, and we distinguish two cases: a) the mesososcopic cells are fixed in space, as appropriate for solids; b) they move with the particles they contain, as in presence of convection, which seems to be our case, cf Refs.[37, 38]. This, does not exclude the existence of the hydrodynamic limit for different 1D systems or under different boundary conditions
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