Numerical determination of entropy associated with excess heat in steady-state thermodynamics

Chiba, Yoshiyuki; Nakagawa, Naoko

doi:10.1103/physreve.94.022115

Cited by 13 publications

(11 citation statements)

References 27 publications

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“…Nevertheless, one can continue to seek a possible framework without considering certain phenomena. Indeed, for a specific model of heat conduction, the extended entropy was numerically estimated [66], which suggests that the extended entropy is close to the spatial integration of the local equilibrium entropy density. Since the extended entropy can be obtained in experiments, a natural question is "What is temperature?"…”

Section: Extended Framework Of Thermodynamicsmentioning

confidence: 83%

Global Thermodynamics for Heat Conduction Systems

Nakagawa

Sasa

2019

J Stat Phys

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We propose the concept of global temperature for spatially non-uniform heat conduction systems. With this novel quantity, we present an extended framework of thermodynamics for the whole system such that the fundamental relation of thermodynamics holds, which we call "global thermodynamics" for heat conduction systems. Associated with this global thermodynamics, we formulate a variational principle for determining thermodynamic properties of the liquid-gas phase coexistence in heat conduction, which corresponds to the natural extension of the Maxwell construction for equilibrium systems. We quantitatively predict that the temperature of the liquid-gas interface deviates from the equilibrium transition temperature. This result indicates that a super-cooled gas stably appears near the interface.

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Section: Extended Framework Of Thermodynamicsmentioning

confidence: 83%

Global Thermodynamics for Heat Conduction Systems

Nakagawa

Sasa

2019

J Stat Phys

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“…This framework is different from previous theories [59][60][61][62][63]. When constructing generalized thermodynamics, we should carefully study the manner of contact [64][65][66][67]. Last but not least, we wish to extend our theory to describe thermodynamic phases of active matter [68,69] and phase transitions in turbulent flow [2,3].…”

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confidence: 99%

Liquid-Gas Transitions in Steady Heat Conduction

Nakagawa

Sasa

2017

Phys. Rev. Lett.

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We study liquid-gas transitions of heat conduction systems in contact with two heat baths under constant pressure in the linear response regime. On the basis of local equilibrium thermodynamics, we propose an equality with a global temperature, which determines the volume near the equilibrium liquid-gas transition. We find that the formation of the liquid-gas interface is accompanied by a discontinuous change in the volume when increasing the mean temperature of the baths. A supercooled gas near the interface is observed as a stable steady state.PACS numbers: 05.70. Ln,Introduction.-Liquid-gas transitions under constant pressure have been a classical subject of equilibrium thermodynamics [1]. In reality, however, a temperature gradient is formed, and thus the transition properties may be influenced by heat flow. As related experiments, enhanced heat conduction by condensation and evaporation was observed in turbulent systems [2,3]. In order to describe such nonequilibrium phenomena systematically, we first need to establish a thermodynamic theory for phase transitions under heat conduction.As the simplest situation, we consider cases where the pressure and heat flux are spatially homogeneous, which is illustrated in Fig. 1 [7][8][9][10]. Furthermore, since the density profile has to be determined under the constraint of global mass conservation, the variational principle for selecting the steady state, if it exists, should be formulated for the whole system. Such a theory has not been reported yet.Over the last two decades, statistical mechanics of nonequilibrium systems has progressed significantly [11][12][13], owing to the discovery of universal relations associated with the second law of thermodynamics [14][15][16][17][18][19][20]. As examples that may be related to the above problem, we point out extensions of thermodynamic relations [21][22][23][24][25][26], variational formulas associated with large deviation theory [27][28][29][30][31], representations of steady state probability densities [32][33][34], and inequalities stronger than the second law [35][36][37][38]. However, these results are not directly applicable to the analysis of liquid-gas transitions in heat conduction.In this Letter, we generalize an equilibrium variational principle that determines the volume near the liquid-gas transition. Concretely, on the basis of local equilibrium thermodynamics in the linear response regime, we propose the equality (11) with a global temperatureT , the main claim of this Letter, which corresponds to the generalized variational principle. This allows us to obtain the phase diagram of the heat conduction system, which can be examined in experiments.Setup.-We study the system shown in Fig. 1. A heat bath of temperature T 1 is attached to the left end (x = 0) of the system, and a second heat bath of temperature T 2 to the right end (x = L), where T 1 ≤ T 2 is assumed without loss of generality. We focus on cases that T c (p ex ) is far below the liquid-gas critical temperature. The length L of the system is fi...

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“…See Refs. [66][67][68][69][70][71] for studies related to an extended Clausius relation. This is the next subject in developing the theory.…”

Section: Discussionmentioning

confidence: 99%

Stochastic order parameter dynamics for phase coexistence in heat conduction

Sasa,

Nakagawa,

Itami

et al. 2019

Preprint

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We propose a stochastic order parameter model for describing phase coexistence in steady heat conduction near equilibrium. By analyzing the stochastic dynamics with a non-equilibrium adiabatic boundary condition, where total energy is conserved over time, we derive a variational principle that determines thermodynamic properties in non-equilibrium steady states. The resulting variational principle indicates that the temperature of the interface between the ordered region and the disordered region becomes greater (less) than the equilibrium transition temperature in the linear response regime when the thermal conductivity in the ordered region is less (greater) than that in the disordered region. This means that a super-heated ordered (super-cooled disordered) state appears near the interface, which was predicted by an extended framework of thermodynamics proposed in [N. Nakagawa and S.-i. Sasa, Liquid-gas transitions in steady heat conduction, Phys. Rev. Lett. 119, 260602, (2017).]

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Numerical determination of entropy associated with excess heat in steady-state thermodynamics

Cited by 13 publications

References 27 publications

Global Thermodynamics for Heat Conduction Systems

Global Thermodynamics for Heat Conduction Systems

Liquid-Gas Transitions in Steady Heat Conduction

Stochastic order parameter dynamics for phase coexistence in heat conduction

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