scholarly journals Clausius' entropy revisited

2014 ◽  
Vol 28 (09) ◽  
pp. 1450073 ◽  
Author(s):  
E. G. D. Cohen ◽  
R. L. Merlino
Keyword(s):  
Equilibrium State ◽  
Entropy Production ◽  
Nonequilibrium Thermodynamics ◽  
Local Equilibrium ◽  
Irreversible Processes ◽  
Local Equilibrium State

Conventional nonequilibrium thermodynamics is mainly concerned with systems in local equilibrium and their entropy production, due to the irreversible processes which take place in these systems. In this paper, fluids will be considered in a state of local equilibrium. We argue that the main feature of such systems is not the entropy production, but the organization of the flowing currents in such systems. These currents do not only have entropy production, but must also have an organization needed to flow in a certain direction. It is the latter, which is the source of the equilibrium entropy, when the fluid goes from a local equilibrium state to an equilibrium state. This implies a transmutation of the local equilibrium currents' organization into the equilibrium entropy. Alternatively, when a fluid goes from an equilibrium state to a local equilibrium state, its entropy transmutes into the organization of the currents of that state.

scholarly journals Thermodynamic aspects of describing the contribution of spontaneous magnetism of electrons to the Hall resistance

2018 ◽  
Vol 185 ◽  
pp. 01017 ◽  
Author(s):  
Vsevolod Okulov ◽  
Evgeny Pamyatnykh
Keyword(s):  
Equilibrium State ◽  
Spontaneous Magnetization ◽  
Local Equilibrium ◽  
Electron System ◽  
Hall Resistance ◽  
Orbital Interaction ◽  
Spin Orbital ◽  
Conduction Current ◽  
Local Equilibrium State ◽  
Current Densities

On the base of the analysis of quantum-statistical description of the magnetization of electron system containing the spontaneous spin polarization contribution there were found the magnetization and conduction current densities in equilibrium state. It has been shown that equilibrium surface conduction current ensures realization of demagnetization effects but in local equilibrium state determines local equilibrium part of the Hall conductivity. As a result one is given the justification of influence of the spontaneous magnetization on galvanomagnetic effects, which is not related to spin-orbital interaction.

Dirac structures and variational formulation of port-Dirac systems in nonequilibrium thermodynamics

2020 ◽  
Vol 37 (4) ◽  
pp. 1298-1347
Author(s):  
François Gay-Balmaz ◽  
Hiroaki Yoshimura
Keyword(s):  
Entropy Production ◽  
Variational Formulation ◽  
Nonequilibrium Thermodynamics ◽  
Open Systems ◽  
Ideal Gas ◽  
Irreversible Processes ◽  
Lagrangian Systems ◽  
Specific Class ◽  
Dirac Structures ◽  
Dirac Systems

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.

Ostwald´s Rule and the Principle of the Shortest Way

2010 ◽  
Vol 224 (06) ◽  
pp. 929-934 ◽  
Author(s):  
Herbert W. Zimmermann
Keyword(s):  
Melting Point ◽  
Equilibrium State ◽  
Entropy Production ◽  
Thermodynamic Stability ◽  
Lagrange Equation ◽  
Classical Mechanics ◽  
Geodesic Line ◽  
Final Equilibrium State ◽  
Relevant Variables ◽  
Non Equilibrium

AbstractWe consider a substance X with two monotropic modifications 1 and 2 of different thermodynamic stability ΔH1 < ΔH2. Ostwald´s rule states that first of all the instable modification 1 crystallizes on cooling down liquid X, which subsequently turns into the stable modification 2. Numerous examples verify this rule, however what is its reason? Ostwald´s rule can be traced back to the principle of the shortest way. We start with Hamilton´s principle and the Euler-Lagrange equation of classical mechanics and adapt it to thermodynamics. Now the relevant variables are the entropy S, the entropy production P = dS/dt, and the time t. Application of the Lagrangian F(S, P, t) leads us to the geodesic line S(t). The system moves along the geodesic line on the shortest way I from its initial non-equilibrium state i of entropy Si to the final equilibrium state f of entropy Sf. The two modifications 1 and 2 take different ways I1 and I2. According to the principle of the shortest way, I1 < I2 is realized in the first step of crystallization only. Now we consider a supercooled sample of liquid X at a temperature T just below the melting point of 1 and 2. Then the change of entropy ΔS1 = Sf 1 - Si 1 on crystallizing 1 can be related to the corresponding chang of enthalpy by ΔS1 = ΔH1/T. Now it can be shown that the shortest way of crystallization I1 corresponds under special, well-defined conditions to the smallest change of entropy ΔS1 < ΔS2 and thus enthalpy ΔH1 < ΔH2. In other words, the shortest way of crystallization I1 really leads us to the instable modification 1. This is Ostwald´s rule.

scholarly journals Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 881 ◽  
Author(s):  
Karl Hoffmann ◽  
Kathrin Kulmus ◽  
Christopher Essex ◽  
Janett Prehl
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Irreversible Processes ◽  
Entropy Production Rate ◽  
Continuous Space ◽  
One Dimensional ◽  
Fractional Diffusion Equations ◽  
And Diffusion

The entropy production rate is a well established measure for the extent of irreversibility in a process. For irreversible processes, one thus usually expects that the entropy production rate approaches zero in the reversible limit. Fractional diffusion equations provide a fascinating testbed for that intuition in that they build a bridge connecting the fully irreversible diffusion equation with the fully reversible wave equation by a one-parameter family of processes. The entropy production paradox describes the very non-intuitive increase of the entropy production rate as that bridge is passed from irreversible diffusion to reversible waves. This paradox has been established for time- and space-fractional diffusion equations on one-dimensional continuous space and for the Shannon, Tsallis and Renyi entropies. After a brief review of the known results, we generalize it to time-fractional diffusion on a finite chain of points described by a fractional master equation.

scholarly journals Time–energy uncertainty principle for irreversible heat engines

2020 ◽  
Vol 378 (2170) ◽  
pp. 20190171 ◽  
Author(s):  
Rudolf Hanel ◽  
Petr Jizba
Keyword(s):  
Uncertainty Principle ◽  
Nonequilibrium Thermodynamics ◽  
Real Life ◽  
Ideal Gas ◽  
Irreversible Processes ◽  
Bohr Radius ◽  
Heat Engines ◽  
Working Medium ◽  
Semi Empirical ◽  
The Ideal

Even though irreversibility is one of the major hallmarks of any real-life process, an actual understanding of irreversible processes remains still mostly semi-empirical. In this paper, we formulate a thermodynamic uncertainty principle for irreversible heat engines operating with an ideal gas as a working medium. In particular, we show that the time needed to run through such an irreversible cycle multiplied by the irreversible work lost in the cycle is bounded from below by an irreducible and process-dependent constant that has the dimension of an action. The constant in question depends on a typical scale of the process and becomes comparable to Planck’s constant at the length scale of the order Bohr radius, i.e. the scale that corresponds to the smallest distance on which the ideal gas paradigm realistically applies. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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