Thermodynamic relations in a driven lattice gas: Numerical experiments

Hayashi, Kumiko; Sasa, Shin Ichi

doi:10.1103/physreve.68.035104

Cited by 32 publications

(65 citation statements)

References 11 publications

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“…The equalization of the chemical potential essentially signifies the steady-state current balance between two systems across the contact as encoded in Eq. (9) and moreover this immediately leads to zeroth law under this particular contact dynamics. However, in the above construction, clearly there is breakdown of equivalence between canonical and grandcanonical ensembles and, therefore thermodynamically, the construction is not well defined.…”

Section: A Lattice Gasesmentioning

confidence: 95%

Zeroth law and nonequilibrium thermodynamics for steady states in contact

2015

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We ask what happens when two nonequilibrium systems in steady state are kept in contact and allowed to exchange a quantity, say mass, which is conserved in the combined system. Will the systems eventually evolve to a new stationary state where a certain intensive thermodynamic variable, like equilibrium chemical potential, equalizes following the zeroth law of thermodynamics and, if so, under what conditions is it possible? We argue that an equilibriumlike thermodynamic structure can be extended to nonequilibrium steady states having short-ranged spatial correlations, provided that the systems interact weakly to exchange mass with rates satisfying a balance condition-reminiscent of a detailed balance condition in equilibrium. The short-ranged correlations would lead to subsystem factorization on a coarse-grained level and the balance condition ensures both equalization of an intensive thermodynamic variable as well as ensemble equivalence, which are crucial for construction of a well-defined nonequilibrium thermodynamics. This proposition is proved and demonstrated in various conserved-mass transport processes having nonzero spatial correlations.

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Section: A Lattice Gasesmentioning

confidence: 95%

Zeroth law and nonequilibrium thermodynamics for steady states in contact

2015

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“…[1], proposed a general scheme of steady-state thermodynamics (SST), including definitions of the chemical potential and pressure in NESS, and developed a theoretical analysis of the driven lattice gas; numerical implementations in driven systems are discussed in Refs. [3,17]. More recently, Chatterjee et al [18] established that in driven systems with particle number conservation and short-ranged correlations, fluctuations in the particle number n s of a subsystem are determined by the functional relation between the variance and the mean of n s .…”

Section: Introductionmentioning

confidence: 97%

Failure of steady-state thermodynamics in nonuniform driven lattice gases

Dickman

2014

Phys. Rev. E

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To be useful, steady-state thermodynamics (SST) must be self-consistent and have predictive value. Consistency of SST was recently verified for driven lattice gases under global weak exchange. Here I verify consistency of SST under local (pointwise) exchange, but only in the limit of a vanishing exchange rate; for a finite exchange rate the coexisting systems have different chemical potentials. I consider the lattice gas with nearest-neighbor exclusion on the square lattice, with nearest-neighbor hopping, and with hopping to both nearest and next-nearest neighbors. I show that SST does not predict the coexisting densities under a nonuniform drive or in the presence of a nonuniform density provoked by a hard wall or nonuniform transition rates. The steady-state chemical potential profile is, moreover, nonuniform at coexistence, contrary to the basic principles of thermodynamics. Finally, I discuss examples of a pair of systems possessing identical steady states but which do not coexist when placed in contact. The results of these studies confirm the validity of SST for coexistence between spatially uniform systems but cast serious doubt on its consistency and predictive value in systems with a finite rate of particle exchange between coexisting regions exhibiting a nonuniform particle density.

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“…For any fixed value of b R the minimum and the maximum accessible values of α, for which one can have exact FSS with rate functions u R,L (n) given by Eq. (18)- (20) are respectively…”

Section: Condensationmentioning

confidence: 99%

“…It is being considered as a reasonably good model for mass transport processes [16] and sandpile dynamics [17,18], reconstituting polymers [19] etc. Being an analytically tractable driven diffusive system, ZRP and related models have become a test ground for development of non-equilibrium thermodynamics [20]. These models also help in understanding experiments on shaken granular gases [21], dynamics of growing networks [22], aggregation of active filament bundles [23], wealth condensation [24], jamming in traffic flow [25], quantum gravity [26] etc.…”

Section: Introductionmentioning

confidence: 99%

Zero range and finite range processes with asymmetric rate functions

Chatterjee

Mohanty

2017

J. Stat. Mech.

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Abstract. We introduce and solve exactly a class of interacting particle systems in one dimension where particles hop asymmetrically. In its simplest form, namely asymmetric zero range process (AZRP), particles hop on a one dimensional periodic lattice with asymmetric hop rates; the rates for both right and left moves depend only on the occupation at the departure site but their functional forms are different. We show that AZRP leads to a factorized steady state (FSS) when its rate-functions satisfy certain constraints. We demonstrate with explicit examples that AZRP exhibits certain interesting features which were not possible in usual zero range process. Firstly, it can undergo a condensation transition depending on how often a particle makes a right move compared to a left one and secondly, the particle current in AZRP can reverse its direction as density is changed. We show that these features are common in other asymmetric models which have FSS, like the asymmetric misanthrope process where rate functions for right and left hops are different, and depend on occupation of both the departure and the arrival site. We also derive sufficient conditions for having cluster-factorized steady states for finite range process with such asymmetric rate functions and discuss possibility of condensation there.Keywords: Zero-range processes, Non-equilibrium processes, Exact results Zero range and finite range processes with asymmetric rate functions 2

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Thermodynamic relations in a driven lattice gas: Numerical experiments

Cited by 32 publications

References 11 publications

Zeroth law and nonequilibrium thermodynamics for steady states in contact

Zeroth law and nonequilibrium thermodynamics for steady states in contact

Failure of steady-state thermodynamics in nonuniform driven lattice gases

Zero range and finite range processes with asymmetric rate functions

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