What is a Simple System?*

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Gian Paolo Beretta ◽  
Elias P. Gyftopoulos
Keyword(s):  
Thermodynamic Equilibrium ◽  
Stable Equilibrium ◽  
Equilibrium States ◽  
Simple System

We discuss relations among properties of systems that consist of any amounts of constituents (including one particle), that have volume as the only parameter, and that are in thermodynamic equilibrium or stable equilibrium states. For large amounts of constituents, we introduce the concept of a simple system, and derive additional relations among properties.

scholarly journals Metastable and stable equilibrium states of stellar electron-nuclear plasmas

2005 ◽  
Vol 336 (4-5) ◽  
pp. 370-377 ◽  
Author(s):  
F. Ferro ◽  
A. Lavagno ◽  
P. Quarati
Keyword(s):  
Stable Equilibrium ◽  
Equilibrium States

What is Diffusion?

1994 ◽  
Vol 116 (2) ◽  
pp. 136-139 ◽  
Author(s):  
E. P. Gyftopoulos ◽  
M. I. Flik ◽  
G. P. Beretta
Keyword(s):  
Stable Equilibrium ◽  
Equilibrium States ◽  
Diffusion Interaction ◽  
Energy Entropy ◽  
Two Systems ◽  
Interacting Systems ◽  
Pass Through

In earlier publications, heat Q← is defined as an interaction that is entirely distinguishable from work W→. The energy exchanged Q← is TQ times the entropy exchanged S←, where TQ is the almost common temperature of the interacting systems. Here, we define diffusion as another interaction that is entirely distinguishable from both work and heat, and that involves exchanges of energy, entropy, and amount of a constituent. It is an interaction between two systems A and B that pass through stable equilibrium states while their respective parameters remain fixed, and that have almost equal temperatures TA ≈ TB ≈ TD and almost equal total potentials μA ≈ μB ≈ μD of the diffusing constituent. The exchanges of entropy S→, energy E→, and amount of constituent n→ out of one system satisfy the relation S→ = (E→ −μDn→)/TD. In the limit of n→ = 0, a diffusion interaction becomes heat.

scholarly journals One of the possible mechanisms for generating the seismic mode “drumbeats” when moving the Kizimen Volcano viscous lava flow along the slope in 2011-2012

2020 ◽  
Vol 2 (3) ◽  
pp. 43-56
Author(s):  
Alexandra Shakirova ◽  
Pavel Firstov ◽  
Mikhail Lemzikov
Keyword(s):  
Lava Flow ◽  
Phenomenological Model ◽  
Stable Equilibrium ◽  
Equilibrium States ◽  
Dynamic Parameters ◽  
Volcano Eruption ◽  
The World ◽  
Magma System ◽  
First Time

"Drumbeats" is an unusual seismic mode consisting of volcanic micro-earthquakes with monotonous waveforms (multiplets) that are recorded from tens of minutes to months. Due to the quasi-regularity of the occurrence of earthquakes, the mode was called "drumbeats". The "drumbeats" mode is registered when individual blocks are squeezed out on the extrusive domes of andesite and dacite volcanoes of the world and occurs at stable equilibrium states in the channel-magma system during an eruption. For the first time in the world practice of volcanological research, the "drumbeats" mode was registered, accompanying the movement of a viscous lava flow with a volume of 0.3 km3 of the Kizimen volcano eruption in 2010-2013. The paper considers kinematic and dynamic parameters of micro-earthquakes of the "drumbeats" mode, their mechanisms, and offers a phenomenological model for generating the "drumbeats" mode that occurs when a lava flow moves along the slope of the Kizimen volcano.

Thermodynamic Definition and Quantum-Theoretic Pictorial Illustration of Entropy

1998 ◽  
Vol 120 (2) ◽  
pp. 154-160 ◽  
Author(s):  
E. P. Gyftopoulos
Keyword(s):  
Equilibrium State ◽  
Thermodynamic Equilibrium ◽  
Stable Equilibrium ◽  
Variable Temperature ◽  
Cyclic Change ◽  
Stable Equilibrium State ◽  
Change Of State ◽  
Laws Of Thermodynamics ◽  
External Forces ◽  
Work Done

Cannot analyzed an engine operating between two reservoirs. Through a peculiar mode of reasoning, he found the correct optimum shaft work done during a cyclic change of state of the engine. Clausius justified Carnot’s result by enunciating two laws of thermodynamics, and introducing the concept of entropy as a ratio of heat and temperature of a thermodynamic equilibrium state. In this paper, we accomplish five purposes: (i) We consider a Carnot engine. By appropriate algebraic manipulations we express Carnot’s optimum shaft work in terms of available energies or exergies of the end states of one reservoir with respect to the other, and Clausius’ entropy S in terms of the energies and available energies of the same and states. (ii) We consider the optimum shaft work done during a cyclic change of state of an engine operating between a reservoir, and a system with fixed amounts of constituents and fixed volume, but variable temperature. We express the optimum shaft work in terms of the available energies of the end states of the system, and Clausius’ entropy in terms of the energies and available energies of the same end states. Formally, the entropy expression is identical to that found for the Carnot engine, except that here the change of state of the system is not isothermal. (iii) We consider the optimum shaft work done during a cyclic change of state of a general engine operating between a reservoir R and system A which initially is in any state A1, stable or thermodynamic equilibrium or not stable equilibrium. In state A1, the values of the amounts of constituents are n1, and the value of the volume is V1 whereas, in the final state A0, n0 ≠ n1 and V0 ≠ V1 Using the laws of thermodynamics presented by Gyftopoulos and Beretta, we prove that such an optimum exists, call it generalized available energy with respect to R, and use it together with the energy to define a new property Σ1 We note that the expression for Σ is formally identical to and satisfies the same criteria as Clausius’ entropy S. The only difference is that Σ applies to all states, whereas Clausius’ S applies only to stable equilibrium states. So we call Σ entropy and denote it by S (iv) We use the unified quantum theory of mechanics and thermodynamics developed by Hatsopoulos and Gyftopoulos, and find a quantum theoretic expression for S in terms of the density operator ρ that yields all the probabilities associated with measurement results. (v) We note that the quantumtheoritic expression for S can be interpreted as a measure of the shape of an atom, molecule, or other system because ρ can be though of as such a shape, and provide pictorial illustrations of this interpretation. For given values of energy E, amounts of constituents n, and volume V, the value of the measure is zero for all shapes that correspond to projectors (wave functions), positive for density operators that are not projectors, and the largest for the ρ that corresponds to the unique stable equilibrium state determined by the given E, n, and V. Accordingly, spontaneous entropy generation occurs as a system adapts its shape to conform to the internal and external forces. Beginning with an arbitrary initial ρ this adaptation continues only until no further spontaneous change of shape can occur, that is, only until a stable equilibrium state is reached.

A unified quantum theory of mechanics and thermodynamics. Part IIb. Stable equilibrium states

1976 ◽  
Vol 6 (4) ◽  
pp. 439-455 ◽  
Author(s):  
George N. Hatsopoulos ◽  
Elias P. Gyftopoulos
Keyword(s):  
Quantum Theory ◽  
Stable Equilibrium ◽  
Equilibrium States

ON ASYMPTOTICALLY STABILIZING THE RABINOVICH DYNAMICAL SYSTEM

2012 ◽  
Vol 09 (05) ◽  
pp. 1220008 ◽  
Author(s):  
RAMONA A. TUDORAN
Keyword(s):  
Dynamical System ◽  
Stable Equilibrium ◽  
Equilibrium States

In this paper we give a method to stabilize asymptotically the nontrivial Lyapunov stable equilibrium states of the Rabinovich dynamical system.

ON ASYMPTOTICALLY STABILIZING THE PLANAR MOTIONS OF AN AUTONOMOUS UNDERWATER VEHICLE

2011 ◽  
Vol 08 (07) ◽  
pp. 1455-1464
Author(s):  
ŞTEFAN NICOARĂ
Keyword(s):  
Stable Equilibrium ◽  
Autonomous Underwater Vehicle ◽  
Underwater Vehicle ◽  
Equilibrium States ◽  
Planar Motions

In this paper we give a method to stabilize asymptotically the Lyapunov stable equilibrium states of a system describing the planar motions of an autonomous underwater vehicle.

Sign in / Sign up

Export Citation Format

Share Document