The Experts below are selected from a list of 291 Experts worldwide ranked by ideXlab platform
Hiroaki Yoshimura - One of the best experts on this subject based on the ideXlab platform.
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Dirac structures and variational formulation of port-Dirac systems in Nonequilibrium Thermodynamics
IMA Journal of Mathematical Control and Information, 2020Co-Authors: François Gay-balmaz, Hiroaki YoshimuraAbstract:Abstract The notion of implicit port-Lagrangian systems for nonholonomic mechanics was proposed in Yoshimura & Marsden (2006a, J. Geom. Phys., 57, 133–156; 2006b, J. Geom. Phys., 57, 209–250; 2006c, Proc. of the 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto) as a Lagrangian analogue of implicit port-Hamiltonian systems. Such port-systems have an interconnection structure with ports through which power is exchanged with the exterior and which can be modeled by Dirac structures. In this paper, we present the notions of implicit port-Lagrangian systems and port-Dirac dynamical systems in Nonequilibrium Thermodynamics by generalizing the Dirac formulation to the case allowing irreversible processes, both for closed and open systems. Port-Dirac systems in Nonequilibrium Thermodynamics can be also deduced from a variational formulation of Nonequilibrium Thermodynamics for closed and open systems introduced in Gay-Balmaz & Yoshimura (2017a, J. Geom. Phys., 111, 169–193; 2018a, Entropy, 163, 1–26). This is a type of Lagrange–d’Alembert principle for the specific class of nonholonomic systems with nonlinear constraints of thermodynamic type, which are associated to the entropy production equation of the system. We illustrate our theory with some examples such as a cylinder-piston with ideal gas, an electric circuit with entropy production due to a resistor and an open piston with heat and matter exchange with the exterior.
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From variational to bracket formulations in Nonequilibrium Thermodynamics of simple systems
Journal of Geometry and Physics, 2020Co-Authors: François Gay-balmaz, Hiroaki YoshimuraAbstract:A variational formulation for Nonequilibrium Thermodynamics was recently proposed in [7, 8] for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include irreversible processes. In this paper, we show that this variational formulation yields a constructive and systematic way to derive from a unified perspective several bracket formulations for Nonequilibrium Thermodynamics proposed earlier in the literature, such as the single generator bracket and the double generator bracket. In the case of a linear relation between the thermodynamic fluxes and the thermodynamic forces, the metriplectic or GENERIC brackets are recovered. A similar development has been presented for continuum systems in [6] and applied to multicomponent fluids.
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GSI - From Variational to Bracket Formulations in Nonequilibrium Thermodynamics of Simple Systems
Lecture Notes in Computer Science, 2019Co-Authors: François Gay-balmaz, Hiroaki YoshimuraAbstract:A variational formulation for Nonequilibrium Thermodynamics was recently proposed in [7, 8] for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include irreversible processes. In this paper, we show that this variational formulation yields a constructive and systematic way to derive from a unified perspective several bracket formulations for Nonequilibrium Thermodynamics proposed earlier in the literature, such as the single generator bracket and the double generator bracket. In the case of a linear relation between the thermodynamic fluxes and the thermodynamic forces, the metriplectic or GENERIC brackets are recovered. A similar development has been presented for continuum systems in [6] and applied to multicomponent fluids.
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From variational to bracket formulations in Nonequilibrium Thermodynamics of simple systems
arXiv: Mathematical Physics, 2019Co-Authors: François Gay-balmaz, Hiroaki YoshimuraAbstract:A variational formulation for Nonequilibrium Thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include irreversible processes. In this paper, we show that this variational formulation yields a constructive and systematic way to derive from a unified perspective several bracket formulations for Nonequilibrium Thermodynamics proposed earlier in the literature, such as the single generator bracket and the double generator bracket. In the case of a linear relation between the thermodynamic fluxes and the thermodynamic forces, the metriplectic or GENERIC bracket is recovered. We also show how the processes of reduction by symmetry can be applied to these brackets. In the reduced setting, we also consider the case in which the coadjoint orbits are preserved and explain the link with double bracket dissipation. A similar development has been presented for continuum systems in \cite{ElGB2019} and applied to multicomponent fluids.
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From Lagrangian Mechanics to Nonequilibrium Thermodynamics: A Variational Perspective
Entropy, 2019Co-Authors: François Gay-balmaz, Hiroaki YoshimuraAbstract:In this paper, we survey our recent results on the variational formulation of Nonequilibrium Thermodynamics for the finite dimensional case of discrete systems as well as for the infinite dimensional case of continuum systems. Starting with the fundamental variational principle of classical mechanics, namely, Hamilton's principle, we show, with the help of thermodynamic systems with gradually increasing level complexity, how to systematically extend it to include irreversible processes. In the finite dimensional cases, we treat systems experiencing the irreversible processes of mechanical friction, heat and mass transfer, both in the adiabatically closed and in the open cases. On the continuum side, we illustrate our theory with the example of multicomponent Navier-Stokes-Fourier systems.
François Gay-balmaz - One of the best experts on this subject based on the ideXlab platform.
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Dirac structures and variational formulation of port-Dirac systems in Nonequilibrium Thermodynamics
IMA Journal of Mathematical Control and Information, 2020Co-Authors: François Gay-balmaz, Hiroaki YoshimuraAbstract:Abstract The notion of implicit port-Lagrangian systems for nonholonomic mechanics was proposed in Yoshimura & Marsden (2006a, J. Geom. Phys., 57, 133–156; 2006b, J. Geom. Phys., 57, 209–250; 2006c, Proc. of the 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto) as a Lagrangian analogue of implicit port-Hamiltonian systems. Such port-systems have an interconnection structure with ports through which power is exchanged with the exterior and which can be modeled by Dirac structures. In this paper, we present the notions of implicit port-Lagrangian systems and port-Dirac dynamical systems in Nonequilibrium Thermodynamics by generalizing the Dirac formulation to the case allowing irreversible processes, both for closed and open systems. Port-Dirac systems in Nonequilibrium Thermodynamics can be also deduced from a variational formulation of Nonequilibrium Thermodynamics for closed and open systems introduced in Gay-Balmaz & Yoshimura (2017a, J. Geom. Phys., 111, 169–193; 2018a, Entropy, 163, 1–26). This is a type of Lagrange–d’Alembert principle for the specific class of nonholonomic systems with nonlinear constraints of thermodynamic type, which are associated to the entropy production equation of the system. We illustrate our theory with some examples such as a cylinder-piston with ideal gas, an electric circuit with entropy production due to a resistor and an open piston with heat and matter exchange with the exterior.
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From variational to bracket formulations in Nonequilibrium Thermodynamics of simple systems
Journal of Geometry and Physics, 2020Co-Authors: François Gay-balmaz, Hiroaki YoshimuraAbstract:A variational formulation for Nonequilibrium Thermodynamics was recently proposed in [7, 8] for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include irreversible processes. In this paper, we show that this variational formulation yields a constructive and systematic way to derive from a unified perspective several bracket formulations for Nonequilibrium Thermodynamics proposed earlier in the literature, such as the single generator bracket and the double generator bracket. In the case of a linear relation between the thermodynamic fluxes and the thermodynamic forces, the metriplectic or GENERIC brackets are recovered. A similar development has been presented for continuum systems in [6] and applied to multicomponent fluids.
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GSI - From Variational to Bracket Formulations in Nonequilibrium Thermodynamics of Simple Systems
Lecture Notes in Computer Science, 2019Co-Authors: François Gay-balmaz, Hiroaki YoshimuraAbstract:A variational formulation for Nonequilibrium Thermodynamics was recently proposed in [7, 8] for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include irreversible processes. In this paper, we show that this variational formulation yields a constructive and systematic way to derive from a unified perspective several bracket formulations for Nonequilibrium Thermodynamics proposed earlier in the literature, such as the single generator bracket and the double generator bracket. In the case of a linear relation between the thermodynamic fluxes and the thermodynamic forces, the metriplectic or GENERIC brackets are recovered. A similar development has been presented for continuum systems in [6] and applied to multicomponent fluids.
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From variational to bracket formulations in Nonequilibrium Thermodynamics of simple systems
arXiv: Mathematical Physics, 2019Co-Authors: François Gay-balmaz, Hiroaki YoshimuraAbstract:A variational formulation for Nonequilibrium Thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include irreversible processes. In this paper, we show that this variational formulation yields a constructive and systematic way to derive from a unified perspective several bracket formulations for Nonequilibrium Thermodynamics proposed earlier in the literature, such as the single generator bracket and the double generator bracket. In the case of a linear relation between the thermodynamic fluxes and the thermodynamic forces, the metriplectic or GENERIC bracket is recovered. We also show how the processes of reduction by symmetry can be applied to these brackets. In the reduced setting, we also consider the case in which the coadjoint orbits are preserved and explain the link with double bracket dissipation. A similar development has been presented for continuum systems in \cite{ElGB2019} and applied to multicomponent fluids.
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From Lagrangian Mechanics to Nonequilibrium Thermodynamics: A Variational Perspective
Entropy, 2019Co-Authors: François Gay-balmaz, Hiroaki YoshimuraAbstract:In this paper, we survey our recent results on the variational formulation of Nonequilibrium Thermodynamics for the finite dimensional case of discrete systems as well as for the infinite dimensional case of continuum systems. Starting with the fundamental variational principle of classical mechanics, namely, Hamilton's principle, we show, with the help of thermodynamic systems with gradually increasing level complexity, how to systematically extend it to include irreversible processes. In the finite dimensional cases, we treat systems experiencing the irreversible processes of mechanical friction, heat and mass transfer, both in the adiabatically closed and in the open cases. On the continuum side, we illustrate our theory with the example of multicomponent Navier-Stokes-Fourier systems.
Yaşar Demirel - One of the best experts on this subject based on the ideXlab platform.
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Nonequilibrium Thermodynamics (Second Edition) - 14 – Nonequilibrium Thermodynamics APPROACHES
Nonequilibrium Thermodynamics, 2014Co-Authors: Yaşar DemirelAbstract:Linear Nonequilibrium Thermodynamics has some fundamental limitations: (1) it does not incorporate mechanisms into its formulation, nor does it provide values for the phenomenological coefficients, and (2) it is based on the local-equilibrium hypothesis, and therefore it is confined to systems in the vicinity of equilibrium. Also, properties not needed or defined in equilibrium may influence the thermodynamic relations in Nonequilibrium situations. For example, the density may depend on the shearing rate in addition to temperature and pressure. The local-equilibrium hypothesis holds only for linear phenomenological relations, low frequencies, and long wavelengths, which makes the application of the linear Nonequilibrium Thermodynamics theory limited for chemical reactions. In the following sections, some of the attempts that have been made to overcome these limitations are summarized.
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Nonequilibrium Thermodynamics (Second Edition) - Fundamentals of Nonequilibrium Thermodynamics
Nonequilibrium Thermodynamics, 2014Co-Authors: Yaşar DemirelAbstract:Physical systems identified by permanently stable and reversible behavior are rare. Unstable phenomena result from inherent fluctuations of the respective state variables. Near a global equilibrium, the fluctuations do not disturb the equilibrium; the trend toward equilibrium is distinguished by asymptotically vanishing dissipative contributions. In contrast, Nonequilibrium states can amplify the fluctuations, and any local disturbances can even move the whole system into an unstable or metastable state. Kinetic and statistical models often require more detailed information than is available to describe Nonequilibrium systems. Therefore, it may be advantageous to have a phenomenological approach with thermodynamic principles to describe natural processes. Such an approach is the formalism used in Nonequilibrium Thermodynamics to investigate physical, chemical, and biological systems with irreversible processes. In the formalism, the Gibbs equation is a key relation since it combines the first and second laws of Thermodynamics. The Gibbs relation, combined with the general balance equations based on the local thermodynamic equilibrium, determines the rate of entropy production. Onsager developed the basic equations of the Nonequilibrium Thermodynamics theory, and Casimir, Meixner, and Prigogine refined and developed the theory further. This chapter outlines the principles of Nonequilibrium Thermodynamics for systems not far from a global equilibrium. In this region, the transport and rate equations are expressed in linear forms, and the Onsager reciprocal relations are valid. Therefore, sometimes this region is called the linear or Onsager region and the formulations are based on linear Nonequilibrium Thermodynamics theory. In this region, instead of thermodynamic potentials and entropy, a new property called entropy production appears.
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Nonequilibrium Thermodynamics. Transport and Rate Processes in Physical, Chemical and Biological Systems. 4th Edition
2014Co-Authors: Yaşar Demirel, Vincent GerbaudAbstract:Nonequilibrium Thermodynamics: Transport and Rate Processes in Physical, Chemical and Biological Systems, Fourth Edition emphasizes the unifying role of Thermodynamics in analyzing natural phenomena. This updated edition expands on the third edition by focusing on the general balance equations for coupled processes of physical, chemical and biological systems. Updates include stochastic approaches, self-organization criticality, ecosystems, mesoscopic Thermodynamics, constructual law, quantum Thermodynamics, fluctuation theory, information theory, and modeling the coupled biochemical systems. The book also emphasizes Nonequilibrium Thermodynamics tools, such as fluctuation theories, mesoscopic thermodynamic analysis, information theories, and quantum Thermodynamics in describing and designing small scale systems.
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Nonequilibrium Thermodynamics modeling of coupled biochemical cycles in living cells
Journal of Non-newtonian Fluid Mechanics, 2010Co-Authors: Yaşar DemirelAbstract:Living cells represent open, Nonequilibrium, self-organizing, and dissipative systems maintained with the continuous supply of outside and inside material, energy, and information flows. The energy in the form of adenosine triphosphate is utilized in biochemical cycles, transport processes, protein synthesis, reproduction, and performing other biological work. The processes in molecular and cellular biological systems are stochastic in nature with varying spatial and time scales, and bounded with conservation laws, kinetic laws, and thermodynamic constraints, which should be taken into account by any approach for modeling biological systems. In component biology, this review focuses on the modeling of enzyme kinetics and fluctuation of single biomolecules acting as molecular motors, while in systems biology it focuses on modeling biochemical cycles and networks in which all the components of a biological system interact functionally over time and space. Biochemical cycles emerge from collective and functional efforts to devise a cyclic flow of optimal energy degradation rate, which can only be described by Nonequilibrium Thermodynamics. Therefore, this review emphasizes the role of Nonequilibrium Thermodynamics through the formulations of thermodynamically coupled biochemical cycles, entropy production, fluctuation theorems, bioenergetics, and reaction-diffusion systems. Fluctuation theorems relate the forward and backward dynamical randomness of the trajectories or paths, bridge the microscopic and macroscopic domains, and link the time-reversible and irreversible descriptions of biological systems. However, many of these approaches are in their early stages of their development and no single computational or experimental technique is able to span all the relevant and necessary spatial and temporal scales. Wide range of experimental and novel computational techniques with high accuracy, precision, coverage, and efficiency are necessary for understanding biochemical cycles.
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Nonequilibrium Thermodynamics (Second Edition) - 12 – STABILITY ANALYSIS
Nonequilibrium Thermodynamics, 2007Co-Authors: Yaşar DemirelAbstract:This chapter reviews the stability analysis based on the conventional Gibbs approach and the Nonequilibrium Thermodynamics theory. It considers the stability of equilibrium, near equilibrium, and far from equilibrium states with some case studies. The entropy production approach for Nonequilibrium systems appears to be more general for stability analysis. One major implication of the Nonequilibrium Thermodynamics theory is the introduction of distance from global equilibrium as a constraint for determining the stability of Nonequilibrium systems. When a system is far from global equilibrium, the possibility of new organized structures of matter arise beyond an instability point. As the Nonequilibrium Thermodynamics theory considers the implications of distance from global equilibrium, it may play a critical role in the understanding of the stability of Nonequilibrium systems. Hydrodynamic instabilities develop mainly by the two competing mechanisms of destabilizing and stabilizing effects, such as kinematic nonlinearity working against viscosity, and gravity competing with a temperature gradient. The classical Gibbs stability theory considers the stability of isolated systems in which energy is totally randomized, and entropy reaches its maximum value, acting as Lyapunov function.
Hans Christian Öttinger - One of the best experts on this subject based on the ideXlab platform.
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Nonequilibrium Thermodynamics: A POWER FUL TOOL FOR SCIENTISTS AND ENGINEERS
Dyna, 2012Co-Authors: Hans Christian ÖttingerAbstract:We present the two-generator framework of Nonequilibrium Thermodynamics with a strong emphasis on fundamental notions rather than mathematical details. The underlying sta- tistical mechanics and the implications for thermodynamically guided simulation techniques are sketched briefly. The usefulness and maturity of the framework are illustrated by reviewing a large number of recent far- from-equilibrium applications, where nonlinearity rules. Finally, we oter some promising perspectives for the future of Nonequilibrium Thermodynamics. I. INTRODUCTION Thermodynamics occurs in the curriculum of every sci- entist or engineer. A typical course on Thermodynamics is restricted to equilibrium phenomena. In most mod- ern courses, Thermodynamics is presented together with statistical mechanics; in many cases, statistical mechan- ics is even presented in the beginning of the course, as if Thermodynamics could be derived from statistical me- chanics. Historically, Thermodynamics has of course been developed well before statistical mechanics, based on a multitude of experimental observations condensed into the fundamental laws of equilibrium Thermodynamics. Moreover, Thermodynamics has the beautiful geometric structure associated with Legendre transformations be- tween pairs of conjugate extensive and intensive variables ("contact structure") and is a full-fledged theory in its own right. Whereas Thermodynamics usually is not among the most popular courses, its laws and tools eventually prove useful to most scientists and engineers. In many applica- tions, however, one would like to go beyond equilibrium Thermodynamics. A typical example is provided by trans- port phenomena (1) which play a most important role in biology, chemical engineering, materials processing, me- chanical engineering, and many other fields. Relaxation phenomena occurring in many areas of application also belong to the world of Nonequilibrium Thermodynamics. Simplification by coarse-graining the description and fo- cusing on the essence of a problem is an important key to successful engineering. A general course on statistical Nonequilibrium Thermodynamics would hence be at least as useful as a course on equilibrium Thermodynamics. The purpose of this article is to address the ques- tion "is Nonequilibrium Thermodynamics ready for sci- entists and engineers?" Should a corresponding course occur in a state-of-the-art curriculum in science and en- gineering? To answer this question we describe a lu- cent framework of Nonequilibrium thermodynamic and its statistical-mechanical foundations. We then provide a number of recent applications of this framework. We finally offer some conclusions and an outlook. This article may be considered as a continuation of the compact review (2) presenting modern Nonequilibrium Thermodynamics to applied scientists and engineers. We hence focus on collecting the literature on the new developments mainly of the last 10 years.
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Lie groups in Nonequilibrium Thermodynamics: Geometric structure behind viscoplasticity
Journal of Non-Newtonian Fluid Mechanics, 2010Co-Authors: Hans Christian ÖttingerAbstract:Poisson brackets provide the mathematical structure required to identify the reversible contribution to dynamic phenomena in Nonequilibrium Thermodynamics. This mathematical structure is deeply linked to Lie groups and their Lie algebras. From the characterization of all the Lie groups associated with a given Lie algebra as quotients of a universal covering group, we obtain a natural classification of rheological models based on the concept of discrete reference states and, in particular, we find a clear-cut and deep distinction between viscoplasticity and viscoelasticity. The abstract ideas are illustrated by a naive toy model of crystal viscoplasticity, but similar kinetic models are also used for modeling the viscoplastic behavior of glasses. We discuss some implications for coarse graining and statistical mechanics.Comment: 11 pages, 1 figure, accepted for publication in J. Non-Newtonian Fluid Mech. Keywords: Elastic-viscoplastic materials, Nonequilibrium Thermodynamics, GENERIC, Lie groups, Reference state
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Dynamic renormalization in the framework of Nonequilibrium Thermodynamics
Physical Review E, 2009Co-Authors: Hans Christian ÖttingerAbstract:We show how the dynamic renormalization of Nonequilibrium systems can be carried out within the general framework of Nonequilibrium Thermodynamics. Whereas the renormalization of Hamiltonians is well known from equilibrium Thermodynamics, the renormalization of dissipative brackets, or friction matrices, is the main new feature for Nonequilibrium systems. Renormalization is a reduction rather than a coarse-graining technique; that is, no new dissipative processes arise in the dynamic renormalization procedure. The general ideas are illustrated for dilute polymer solutions where, in renormalizing bead-spring chain models, dissipative hydrodynamic interactions between different smaller beads contribute to the friction coefficient of a single larger bead.
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Nonequilibrium Thermodynamics of glasses
Physical Review E, 2006Co-Authors: Hans Christian ÖttingerAbstract:We consider the Nonequilibrium Thermodynamics of glasses from various perspectives. For the commonly used equilibriumlike approach based on Gibbs' fundamental form with an additional pair of conjugate variables, we discuss possible choices of the independent out-of-equilibrium variable and we illustrate some implications by concrete results for a well-known exactly solvable lattice model. The choice of variables is further illuminated from the complementary atomistic perspective offered by the inherent-structure formalism. A general formalism of Nonequilibrium Thermodynamics is employed (i) to derive the standard equilibriumlike approach, (ii) to formulate two self-contained levels to describe glassy dynamics and Thermodynamics, and (iii) to offer guidance for future simulations of glasses. The thermodynamic approach suggests to introduce four-point correlation functions associated with structural rearrangements after imposed deformations, which might offer a possibility to detect a growing length scale at the glass transition without employing any dynamic information.
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Nonequilibrium Thermodynamics for open systems.
Physical Review E, 2006Co-Authors: Hans Christian ÖttingerAbstract:We develop the general equation for the Nonequilibrium reversible-irreversible coupling (GENERIC) framework of Nonequilibrium Thermodynamics for open systems. A clear distinction between bulk and boundary contributions to the Poisson and dissipative brackets employed to generate reversible and irreversible contributions to time evolution from energy and entropy allows us to formulate the bulk equations as well as the exchange and interaction with the environment directly. The full brackets keep all the structure and hence the predictive power of the original GENERIC for isolated systems. The straightforward procedure is illustrated for hydrodynamics of open systems. Boltzmann’s kinetic equation is discussed as a further example. In the Appendix, the thermodynamic treatment of surface excess variables at walls and their role in boundary conditions for the bulk variables is exemplified for a diffusion cell.
Massimiliano Esposito - One of the best experts on this subject based on the ideXlab platform.
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Nonequilibrium Thermodynamics of non ideal chemical reaction networks
Journal of Chemical Physics, 2021Co-Authors: Francesco Avanzini, Emanuele Penocchio, Gianmaria Falasco, Massimiliano EspositoAbstract:All current formulations of Nonequilibrium Thermodynamics of open chemical reaction networks rely on the assumption of non-interacting species. We develop a general theory that accounts for interactions between chemical species within a mean-field approach using activity coefficients. Thermodynamic consistency requires that rate equations do not obey standard mass-action kinetics but account for the interactions with concentration dependent kinetic constants. Many features of the ideal formulations are recovered. Crucially, the thermodynamic potential and the forces driving non-ideal chemical systems out of equilibrium are identified. Our theory is general and holds for any mean-field expression of the interactions leading to lower bounded free energies.
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Open questions on Nonequilibrium Thermodynamics of chemical reaction networks
Communications Chemistry, 2020Co-Authors: Massimiliano EspositoAbstract:Chemical reaction networks (CRNs) are prototypical complex systems because reactions are nonlinear and connected in intricate ways, and they are also essential to understand living systems. Here, the author discusses how recent developments in Nonequilibrium Thermodynamics provide new insight on how CRNs process energy and perform sophisticated tasks, and describes open challenges in the field.
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Conservation Laws in Nonequilibrium Thermodynamics
2019Co-Authors: Massimiliano EspositoAbstract:Conservation laws play a key role in shaping dissipation in Nonequilibrium Thermodynamics by identifying conservative and nonconservative thermodynamic forces as well as the right Nonequilibrium potential. I will first demonstrate this finding using stochastic Thermodynamics and then deterministic open chemical reaction networks. Various applications will then be presented.
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Nonequilibrium Thermodynamics and Nose-Hoover Dynamics
The journal of physical chemistry. B, 2010Co-Authors: Massimiliano Esposito, Takaaki MonnaiAbstract:We show that systems driven by an external force and described by Nose−Hoover dynamics allow for a consistent Nonequilibrium Thermodynamics description when the thermostatted variable is initially assumed in a state of canonical equilibrium. By treating the “real” variables as the system and the thermostatted variable as the reservoir, we establish the first and second law of Thermodynamics. As for Hamiltonian systems, the entropy production can be expressed as a relative entropy measuring the system−reservoir correlations established during the dynamics.