“equilibrium”的概念、定义、翻译、参考文献-科学参考

equilibrium

Physics

A state in which a system has its energy distributed in the statistically most probable manner; a state of a system in which forces, influences, reactions, etc., balance each other out so that there is no net change.

A body is in static equilibrium if the resultants of all forces and all couples acting on it are both zero; it may be at rest and will certainly not be accelerated. Such a body at rest is in stable equilibrium if after a slight displacement it returns to its original position—for a body whose weight is the only downward force this will be the case if the vertical line through its centre of gravity always passes through its base. If a slight displacement causes the body to move to a new position, then the body is in unstable equilibrium.

A body is said to be in thermal equilibrium if no net heat exchange is taking place within it or between it and its surroundings. A system is in chemical equilibrium when a reaction and its reverse are proceeding at equal rates. These are examples of dynamic equilibrium, in which activity in one sense or direction is in aggregate balanced by comparable reverse activity.

Mathematics

A particle is in equilibrium when it is at rest and the total force acting on it is zero for all time. These conditions are equivalent to saying that r = r₀ (a constant vector), $\dot{r} = 0$ and $\ddot{r} = 0$ for all time, where r is the position vector of the particle. We then say that r₀ is an equilibrium or equilibrium position.

Consider a rigid body experiencing a system of forces. Let F be the total force and M the moment of the forces about the origin. The rigid body is in equilibrium when it is at rest and F = 0 and M = 0 for all time.

A body, in equilibrium, is in stable equilibrium if, following a small change in its position, it returns to, or remains close to, the equilibrium position. It is in unstable equilibrium if, following a small change in its position, it continues to move further from the equilibrium position. See linear theory of equilibria, Lyapunov stability.

Statistics

A stochastic process is said to be in equilibrium if, for every state of the process and for each time point, the probability of being in that state at the next time point is equal to the probability for the current time point.

Chemistry

A state in which a system has its energy distributed in the statistically most probable manner; a state of a system in which forces, influences, reactions, etc., balance each other out so that there is no net change. A body is said to be in thermal equilibrium if no net heat exchange is taking place within it or between it and its surroundings. A system is in chemical equilibrium when a reaction and its reverse are proceeding at equal rates (see also equilibrium constant). These are examples of dynamic equilibrium, in which activity in one sense or direction is in aggregate balanced by comparable reverse activity.

Chemical Engineering

A condition or state in which a balance exists within a system, which may be physical or chemical. A system is in equilibrium if it shows no tendency to change its properties with time. Static equilibrium occurs if there is no transfer of energy across the system boundary, whereas dynamic equilibrium is when transfer occurs but the net effect of the energy is zero. Thermodynamic equilibrium occurs when there is no heat or work exchange between a body and its surroundings. Chemical equilibrium occurs when a chemical reaction takes place in the forwards direction, when reactants form products at exactly the same rate as the reverse reaction of products revert to their original reactant form.

Geology and Earth Sciences

In geomorphology, a steady state of balance between the processes acting on a landscape and the resisting Earth materials so that over time the geometric shape of the landscape is little changed. Individual land-forms, such as river profiles and hillslopes, may show similar balance. As it is recognized that a perfect balance cannot exist between input and output of energy, the terms ‘quasi-’ and ‘dynamic’ equilibrium are sometimes used. Quasi-equilibrium is an apparent equilibrium which is recognized for short periods of time.

Geography

In physical geography, the state of an open system where the inputs, throughputs, and outputs of energy or matter are in balance. Equilibrium relies on the presence of negative feedback loops within the system (R. Inkpen 2005) and J. Holden (2012) recognizes: ‘static equilibrium (no change over time) or a steady-state equilibrium (short-term fluctuations about a longer-term mean value) while over longer time periods the equilibrium might be dynamic (shorter-term fluctuations with a longer-term mean value that is changing)’. Holden adds ‘the concept of equilibrium has always been somewhat confusing because different people have chosen to identify different types of equilibrium and because the precise meaning is time dependent…Often it depends on where and when you measure something as to whether it will show equilibrium’. Within a system, the equilibrium time is the time required for a system to establish a new steady state after the application of a stimulus or a change in external conditions. Within human geography spatial equilibrium is regional equality, brought about by the interaction of labour moving to high-wage areas and capital moving to regions where wage rates are low, and usually expressed in terms of wages: ‘workers and firms are indifferent among alternative locations as they have eliminated any systematic difference in indirect utility and profits through migration’ (Ottoviano and Perri (2005) J. Econ. Geog. 6, 1.

Economics

An equilibrium can be defined either as a position of balance in the economy or, equivalently, as a situation in which no agent in the economy has any incentive to modify their chosen strategy. The first definition is derived from the perspective of equilibrium occurring when the forces of supply are balanced by the forces of demand. The second definition derives from the theory of games and is illustrated by the equilibrium of an oligopolistic market in which all firms are satisfied with their choice of output level given the choices of their rivals. Proving the existence of equilibrium and demonstrating the welfare properties of equilibrium are important steps in the analysis of an economic model. Equally important is analysis of the uniqueness and stability of equilibrium, and the determination of how changes in exogenous parameters affect the equilibrium (comparative statics). There are several explanations for the emphasis upon equilibrium. Historically, the economy was viewed as self-correcting so that if it were ever pushed away from equilibrium forces exist that would move it back towards equilibrium. The present justifications for focusing upon equilibrium are more pragmatic. The analysis of a model must begin somewhere, and the equilibrium is a natural starting point. Alternatively, the focus can be justified by showing that the equilibrium is the outcome of playing the underlying game correctly. In addition, even if the final focus is on disequilibrium, there is benefit from comparing the properties of points of disequilibrium to those of the equilibrium. Finally, no positions other than those of equilibrium have any obvious claim to prominence. See also competitive equilibrium; general equilibrium; market equilibrium; multiple equilibrium; Nash equilibrium; partial equilibrium; subgame perfect equilibrium.

单词	equilibrium
释义	equilibrium Physics A state in which a system has its energy distributed in the statistically most probable manner; a state of a system in which forces, influences, reactions, etc., balance each other out so that there is no net change. A body is in static equilibrium if the resultants of all forces and all couples acting on it are both zero; it may be at rest and will certainly not be accelerated. Such a body at rest is in stable equilibrium if after a slight displacement it returns to its original position—for a body whose weight is the only downward force this will be the case if the vertical line through its centre of gravity always passes through its base. If a slight displacement causes the body to move to a new position, then the body is in unstable equilibrium. A body is said to be in thermal equilibrium if no net heat exchange is taking place within it or between it and its surroundings. A system is in chemical equilibrium when a reaction and its reverse are proceeding at equal rates. These are examples of dynamic equilibrium, in which activity in one sense or direction is in aggregate balanced by comparable reverse activity. Mathematics A particle is in equilibrium when it is at rest and the total force acting on it is zero for all time. These conditions are equivalent to saying that r = r₀ (a constant vector), $\dot{r} = 0$ and $\ddot{r} = 0$ for all time, where r is the position vector of the particle. We then say that r₀ is an equilibrium or equilibrium position. Consider a rigid body experiencing a system of forces. Let F be the total force and M the moment of the forces about the origin. The rigid body is in equilibrium when it is at rest and F = 0 and M = 0 for all time. A body, in equilibrium, is in stable equilibrium if, following a small change in its position, it returns to, or remains close to, the equilibrium position. It is in unstable equilibrium if, following a small change in its position, it continues to move further from the equilibrium position. See linear theory of equilibria, Lyapunov stability. Statistics A stochastic process is said to be in equilibrium if, for every state of the process and for each time point, the probability of being in that state at the next time point is equal to the probability for the current time point. Chemistry A state in which a system has its energy distributed in the statistically most probable manner; a state of a system in which forces, influences, reactions, etc., balance each other out so that there is no net change. A body is said to be in thermal equilibrium if no net heat exchange is taking place within it or between it and its surroundings. A system is in chemical equilibrium when a reaction and its reverse are proceeding at equal rates (see also equilibrium constant). These are examples of dynamic equilibrium, in which activity in one sense or direction is in aggregate balanced by comparable reverse activity. Chemical Engineering A condition or state in which a balance exists within a system, which may be physical or chemical. A system is in equilibrium if it shows no tendency to change its properties with time. Static equilibrium occurs if there is no transfer of energy across the system boundary, whereas dynamic equilibrium is when transfer occurs but the net effect of the energy is zero. Thermodynamic equilibrium occurs when there is no heat or work exchange between a body and its surroundings. Chemical equilibrium occurs when a chemical reaction takes place in the forwards direction, when reactants form products at exactly the same rate as the reverse reaction of products revert to their original reactant form. Geology and Earth Sciences In geomorphology, a steady state of balance between the processes acting on a landscape and the resisting Earth materials so that over time the geometric shape of the landscape is little changed. Individual land-forms, such as river profiles and hillslopes, may show similar balance. As it is recognized that a perfect balance cannot exist between input and output of energy, the terms ‘quasi-’ and ‘dynamic’ equilibrium are sometimes used. Quasi-equilibrium is an apparent equilibrium which is recognized for short periods of time. Geography In physical geography, the state of an open system where the inputs, throughputs, and outputs of energy or matter are in balance. Equilibrium relies on the presence of negative feedback loops within the system (R. Inkpen 2005) and J. Holden (2012) recognizes: ‘static equilibrium (no change over time) or a steady-state equilibrium (short-term fluctuations about a longer-term mean value) while over longer time periods the equilibrium might be dynamic (shorter-term fluctuations with a longer-term mean value that is changing)’. Holden adds ‘the concept of equilibrium has always been somewhat confusing because different people have chosen to identify different types of equilibrium and because the precise meaning is time dependent…Often it depends on where and when you measure something as to whether it will show equilibrium’. Within a system, the equilibrium time is the time required for a system to establish a new steady state after the application of a stimulus or a change in external conditions. Within human geography spatial equilibrium is regional equality, brought about by the interaction of labour moving to high-wage areas and capital moving to regions where wage rates are low, and usually expressed in terms of wages: ‘workers and firms are indifferent among alternative locations as they have eliminated any systematic difference in indirect utility and profits through migration’ (Ottoviano and Perri (2005) J. Econ. Geog. 6, 1. Economics An equilibrium can be defined either as a position of balance in the economy or, equivalently, as a situation in which no agent in the economy has any incentive to modify their chosen strategy. The first definition is derived from the perspective of equilibrium occurring when the forces of supply are balanced by the forces of demand. The second definition derives from the theory of games and is illustrated by the equilibrium of an oligopolistic market in which all firms are satisfied with their choice of output level given the choices of their rivals. Proving the existence of equilibrium and demonstrating the welfare properties of equilibrium are important steps in the analysis of an economic model. Equally important is analysis of the uniqueness and stability of equilibrium, and the determination of how changes in exogenous parameters affect the equilibrium (comparative statics). There are several explanations for the emphasis upon equilibrium. Historically, the economy was viewed as self-correcting so that if it were ever pushed away from equilibrium forces exist that would move it back towards equilibrium. The present justifications for focusing upon equilibrium are more pragmatic. The analysis of a model must begin somewhere, and the equilibrium is a natural starting point. Alternatively, the focus can be justified by showing that the equilibrium is the outcome of playing the underlying game correctly. In addition, even if the final focus is on disequilibrium, there is benefit from comparing the properties of points of disequilibrium to those of the equilibrium. Finally, no positions other than those of equilibrium have any obvious claim to prominence. See also competitive equilibrium; general equilibrium; market equilibrium; multiple equilibrium; Nash equilibrium; partial equilibrium; subgame perfect equilibrium.
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