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We consider viscous, heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of…

Fluid Dynamics · Physics 2016-04-01 Dieter Bothe , Wolfgang Dreyer

Nonreciprocity, a hallmark of nonequilibrium systems, can generate dynamics not possible near thermodynamic equilibrium, including oscillatory and rotating patterns. The onset of temporal oscillations is often evident in linearized…

Statistical Mechanics · Physics 2026-04-21 Daniel Evans , Yizhi Shen , Ahmad K. Omar

In this and a companion paper we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first…

Chemical Physics · Physics 2014-10-22 Matteo Polettini , Massimiliano Esposito

In this letter we clarify the role of heat flux in the hydrodynamic balance equations in 2D quantum wells, facilitating the formulation of an Onsager relation within the framework of this theory. We find that the Onsager relation is…

Condensed Matter · Physics 2009-10-28 M. W. Wu , H. L. Cui , W. Sun , S. Y. Wu

We investigate a hydrodynamic system of Navier--Stokes/Cahn--Hilliard type, which describes the motion of a two-phase flow of two incompressible fluids with unmatched densities coupled with a soluble chemical species. Derived from Onsager's…

Analysis of PDEs · Mathematics 2025-12-30 Andrea Giorgini , Jingning He , Hao Wu

We derive a linear thermodynamics theory for general Markov dynamics with both steady-state and time-periodic drivings. Expressions for thermodynamic quantities, such as mechanical and chemical work, heat and entropy production are obtained…

Statistical Mechanics · Physics 2019-09-04 Karel Proesmans , Carlos E. Fiore

A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the "Thermodynamic Field Theory" (TFT). The aim of the work was to determine the nonlinear…

Statistical Mechanics · Physics 2015-06-23 Giorgio Sonnino

We present a systematic derivation of thermodynamically consistent hydrodynamic phase field models for compressible viscous fluid mixtures using the generalized Onsager principle. By maintaining momentum conservation while enforcing mass…

Numerical Analysis · Mathematics 2018-09-25 Xueping Zhao , Tiezheng Qian , Qi Wang

In existing linear response theories for adiabatically driven cyclic heat engines, Onsager symmetry is identified only phenomenologically, and a relation between global and local Onsager coefficients, defined over one cycle and at any…

Statistical Mechanics · Physics 2021-05-19 Yuki Izumida

In this paper we clarify the role of heat flux in the hydrodynamic balance equations, facilitating the formulation of an Onsager relation within the framework of this theory. Previously thought to be unobtainable from the present form of…

Condensed Matter · Physics 2009-10-28 M. W. Wu , H. L. Cui , N. J. M. Horing

We formulate nonequilibrium thermodynamics in which intensive variables acquire operational meaning through measurement protocols consistent with local reciprocity. Using physical equilibrium as a reference, conjugate observables are…

Statistical Mechanics · Physics 2026-02-09 Akihisa Ichiki

Starting from the Liouville equation, and using a BBGKY-like hierarchy, we derive a kinetic equation for the point vortex gas in two-dimensional (2D) hydrodynamics, taking two-body correlations and collective effects into account. This…

Statistical Mechanics · Physics 2015-05-30 Pierre-Henri Chavanis

Symmetry relations are manifestations of fundamental principles and constitute cornerstones of modern physics. An example are the Onsager relations between coefficients connecting thermodynamic fluxes and forces, central to transport theory…

Mesoscale and Nanoscale Physics · Physics 2014-12-11 J. Matthews , F. Battista , D. Sanchez , P. Samuelsson , H. Linke

Close to equilibrium, the kinetic coefficients of a thermodynamic system must satisfy a set of symmetry conditions, which follow from the Onsager-Casimir principle. Here, we show that, if a system of hydrodynamic equations is analysed from…

Nuclear Theory · Physics 2023-03-22 Lorenzo Gavassino

Classical thermodynamics contains familiar geometric relations associated with cyclic processes, most notably the identification of mechanical work with the area enclosed by a trajectory in the $(P,V)$ plane. We show that the area laws for…

Statistical Mechanics · Physics 2026-03-25 Eric R. Bittner

We discuss a consequence of time reversal symmetry on thermoelectric effect in nonequilibrium coherent quantum transport. Starting with a quantum version of the fluctuation theorem, we show that there exist universal relations between the…

Mesoscale and Nanoscale Physics · Physics 2010-02-02 Eiki Iyoda , Yasuhiro Utsumi , Takeo Kato

Nonequilibrium steady state of isothermal biochemical cycle kinetics has been extensively studied, but much less investigated under non-isothermal conditions. However, once the heat exchange between subsystems is rather slow, the isothermal…

Chemical Physics · Physics 2016-10-11 Xiao Jin , Hao Ge

In a recent perspective article, Horowitz and Gingrich discuss thermodynamic uncertainty relations that have been derived using "stochastic thermodynamics", a theory based on a hypothesis known as local detailed balance. The authors…

Statistical Mechanics · Physics 2020-03-25 R. Dean Astumian

The theory of linear stochastic thermodynamics is developed for periodically driven systems in contact with a single reservoir. Appropriate thermodynamic forces and fluxes are identified, starting from the entropy production for a Markov…

Statistical Mechanics · Physics 2016-02-26 Karel Proesmans , Bart Cleuren , Christian Van den Broeck

We study nonequilibrium steady states of the one-dimensional discrete nonlinear Schroedinger equation. This system can be regarded as a minimal model for stationary transport of bosonic particles like photons in layered media or cold atoms…

Statistical Mechanics · Physics 2012-08-30 S. Iubini , S. Lepri , A. Politi