Closed, isolated, physical system

In principle any closed isolated physical system can be described as a Markov process by introducing all microscopic variables as components of Y. In fact, the microscopic motion in phase space is deterministic and therefore Markovian, compare (1.3). The physicist s question, however, is whether he can find a small set of variables whose behavior in time can be described as a multicomponent Markov process. The well-known, but still miraculous, experimental fact is that this is so for most many-body systems... 

The present proof is more limited than the one in 3 because we have to assume beforehand that there is a stationary solution that is everywhere positive. For closed, isolated, physical systems one knows that that is so, and we therefore use here the symbol pi for that stationary solution of the master equation. Yet the proof also applies to other cases provided they have no transient states, but the proof does not require detailed balance of any other symmetry relation of the type (4.2). 

Without loss of generality we assume that W is indecomposable. Owing to the symmetry property (4.2) or (6.1) this implies that it cannot be reducible to the form (2.7) either. This would not be a valid conclusion if some of the pi could vanish, but in a closed isolated physical system one knows that all states have a non-zero equilibrium probability. 

For definiteness consider a closed, isolated physical system. If at t = 0 the quantity Y has the precise value y0 the probability density P(y, t) is initially 5(y — y0). It will tend to Pe(y) as t increases. If y0 is macroscopically different from the equilibrium value of Y it means that y0 is far outside the width of Pe(y), because macroscopically observed values are large compared to the equilibrium fluctuations. We also know from experience that the fluctuations remain small during the whole process. That means that P y, t), for each t, is a sharply peaked function of y. The location of this peak is a fairly well-defined number, having an uncertainty of the order of the width of the peak, and is to be identified with the macroscopic value y(t). For definiteness one customarily adopts the more precise definition... 

Suppose we have a closed, isolated physical system whose non-equilibrium behavior is adequately described by a one-step master equation for a single quantity. Then, supposing the quantity is an even function, we know that detailed balance holds, which for a one-step process reads... 

This difficulty does not arise in the case of closed, isolated physical systems, because there the stationary solution is known to be the thermal equilibrium distribution Pe(x), as given by ordinary statistical mechanics. This knowledge implies some information about At and Bij9 but more information is available if also detailed balance (V.6.1) or extended detailed balance (V.6.14) holds. In the following we shall therefore examine the situation specified by the following stipulations. 

When the desired pressure is developed, isolate the system by closing the isolation valve and ensure no physical leakage takes place from all welding joints as well as bolted joints. If any leakage is identified, then release the pressure. After rectification... 

This is true for closed, isolated, finite physical systems under certain restric-... 

Yet it is necessary for a clear understanding to distinguish between the logical status of (3.7) and (3.14). Equation (3.7) is merely the master equation with left-hand side set equal to zero it owes its simple form to the restriction to one-step processes. It has no physical content and applies to open systems as well, and even to non-physical systems, such as populations. On the other hand (3.14) states a physical principle pe is regarded as known from equilibrium statistical mechanics and the equation provides a connection between the transition probabilities r ,g , which must hold if the system is closed and isolated. 

Schweitz was the first to recognize that the definition of pressure is a problem in the physics of an open system. He argued that the classical result based on the properties of a closed, isolated system - a petit ensemble - must be recast in terms of an open system, a system with permeable walls, replacing the petit ensemble with the grand ensemble. This he did for both a classical... 

Thermodynamic description of natural processes usually begins by dividing the world into a system and its exterior, which is the rest of the world. This cannot be done, of course, when one is considering the thermodynamic nature of the entire universe. The definition of a thermodynamic system often depends on the existence of boundaries, boundaries that separate the system of interest from the rest of the world. In understanding the thermodynamic behavior of physical systems, the nature of the interaction between the system and the exterior is important. Accordingly, thermodynamic systems are classified into three types, isolated, closed and open systems according to the way they interact with their exterior (Fig. 1.1). 

From all possible statistical systems the equilibrium closed systems are allocated. For such systems the physical theory, referred to as equilibrium thermodynamics or simply thermodynamics, is well developed. Thermodynamics is the phenomenological doctrine of heat. Classical thermodynamics asserts that the isolated thermodynamic system cannot spontaneously change it s state . This statement is sometimes referred to as the zeroth law of thermodynamics, another assertion of which is that If two thermodynamic systems are in thermodynamic equilibrium with some third body they are in thermodynamic equilibrium with each other . 

I.2.5.I. General introduction. The physical chemistry of closed systems, such as an evacuated line isolated from the pumps, is of course implicit in the general physical chemistry which should be familiar to the readers of... 

Thermodynamic systems are parts of the real world isolated for thermodynamic study. The parts of the real world which are to be isolated here are either natural water systems or certain regions within these systems, depending upon the physical and chemical complexity of the actual situation. The primary objects of classical thermodynamics are two particular kinds of isolated systems adiabatic systems, which cannot exchange either matter or thermal energy with their environment, and closed systems, which cannot exchange matter with their environment. (The closed system may, of course, consist of internal phases which are each open with respect to the transport of matter inside the closed system.) Of these, the closed system, under isothermal and iso-baric conditions, is the one particularly applicable for constructing equilibrium models of actual natural water systems. 

In physics and chemistry we call an ensemble of substances a thermodynamic system consisting of atomic and molecular particles. The system is separated from the surroundings by a boundary interface. The system is called isolated when no transfer is allowed to occur of substances, heat, and work across the boundary interface of the system as shown in Fig. 1.1. The system is called closed when it allows both heat and work to transfer across the interface but is impermeable to substances. The system is called open if it is completely permeable to substances, heat, and work. The open system is the most general and it can be regarded as a part of a closed or isolated system. For instance, the universe is an isolated system, the earth is regarded as a closed system, and a creature such as a human being corresponds to an open system. 

The universe is an excellent paradigm of an isolated and closed system. Ordinarily, events occurring at astronomical time scales may be ignored in the consideration of physical and chemical processes occurring in the laboratory. 

Molecular. At the molecular level the relationship of strength and chemical composition deals with the individual polymeric components that make up the cell wall. The physical and chemical properties of cellulose, hemicelluloses, and lignin play a major role in the chemistry of strength. However, our perceptions of wood polymeric properties are based on isolated polymers that have been removed from the wood system and, therefore, possibly altered. The individual polymeric components may be far more closely associated with one another than has heretofore been believed. 

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