thermodynamic system

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A thermodynamic system is a body of
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
and/or
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visib ...
, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other
thermodynamic Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
systems, or physical systems that are not thermodynamic systems. A wall of a thermodynamic system may be purely notional, when it is described as being 'permeable' to all matter, all radiation, and all forces. A state of a thermodynamic system can be fully described in several different ways, by several different sets of thermodynamic state variables. A widely used distinction is between ''isolated'', ''closed'', and ''open'' thermodynamic systems. An isolated thermodynamic system has walls that are non-conductive of heat and perfectly reflective of all radiation, that are rigid and immovable, and that are impermeable to all forms of matter and all forces. (Some writers use the word 'closed' when here the word 'isolated' is being used.) A closed thermodynamic system is confined by walls that are impermeable to matter, but, by thermodynamic operations, alternately can be made permeable (described as 'diathermal') or impermeable ('adiabatic') to heat, and that, for thermodynamic processes (initiated and terminated by thermodynamic operations), alternately can be allowed or not allowed to move, with system volume change or agitation with internal friction in system contents, as in Joule's original demonstration of the mechanical equivalent of heat, and alternately can be made rough or smooth, so as to allow or not allow heating of the system by friction on its surface. An open thermodynamic system has at least one wall that separates it from another thermodynamic system, which for this purpose is counted as part of the surroundings of the open system, the wall being permeable to at least one chemical substance, as well as to radiation; such a wall, when the open system is in thermodynamic equilibrium, does not sustain a temperature difference across itself. A thermodynamic system is subject to external interventions called thermodynamic operations; these alter the system's walls or its surroundings; as a result, the system undergoes transient
thermodynamic process Classical thermodynamics considers three main kinds of thermodynamic process: (1) changes in a system, (2) cycles in a system, and (3) flow processes. (1)A Thermodynamic process is a process in which the thermodynamic state of a system is change ...
es according to the principles of
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
. Such operations and processes effect changes in the thermodynamic state of the system. When the intensive state variables of its content vary in space, a thermodynamic system can be considered as many systems contiguous with each other, each being a different thermodynamical system. A thermodynamic system may comprise several phases, such as ice, liquid water, and water vapour, in mutual thermodynamic equilibrium, mutually unseparated by any wall; or it may be homogeneous. Such systems may be regarded as 'simple'. A 'compound' thermodynamic system may comprise several simple thermodynamic sub-systems, mutually separated by one or several walls of definite respective permeabilities. It is often convenient to consider such a compound system initially isolated in a state of thermodynamic equilibrium, then affected by a thermodynamic operation of increase of some inter-sub-system wall permeability, to initiate a transient thermodynamic process, so as to generate a final new state of thermodynamic equilibrium. This idea was used, and perhaps introduced, by Carathéodory. In a compound system, initially isolated in a state of thermodynamic equilibrium, a reduction of a wall permeability does not effect a thermodynamic process, nor a change of thermodynamic state. This difference expresses the
Second Law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...
. It illustrates that increase in entropy measures increase in dispersal of energy, due to increase of accessibility of microstates. In equilibrium thermodynamics, the state of a thermodynamic system is a state of
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal State variables, state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
, as opposed to a non-equilibrium state. According to the permeabilities of the walls of a system, transfers of energy and matter occur between it and its surroundings, which are assumed to be unchanging over time, until a state of thermodynamic equilibrium is attained. The only states considered in equilibrium thermodynamics are equilibrium states. Classical thermodynamics includes (a) equilibrium thermodynamics; (b) systems considered in terms of cyclic sequences of processes rather than of states of the system; such were historically important in the conceptual development of the subject. Systems considered in terms of continuously persisting processes described by steady flows are important in engineering. The very existence of thermodynamic equilibrium, defining states of thermodynamic systems, is the essential, characteristic, and most fundamental postulate of thermodynamics, though it is only rarely cited as a numbered law. According to Bailyn, the commonly rehearsed statement of the
zeroth law of thermodynamics The zeroth law of thermodynamics is one of the four principal laws of thermodynamics. It provides an independent definition of temperature without reference to entropy, which is defined in the second law. The law was established by Ralph H. Fowle ...
is a consequence of this fundamental postulate. In reality, practically nothing in nature is in strict thermodynamic equilibrium, but the postulate of thermodynamic equilibrium often provides very useful idealizations or approximations, both theoretically and experimentally; experiments can provide scenarios of practical thermodynamic equilibrium. In equilibrium thermodynamics the state variables do not include fluxes because in a state of thermodynamic equilibrium all fluxes have zero values by definition. Equilibrium thermodynamic processes may involve fluxes but these must have ceased by the time a thermodynamic process or operation is complete bringing a system to its eventual thermodynamic state. Non-equilibrium thermodynamics allows its state variables to include non-zero fluxes, that describe transfers of
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity of matter in a Physical object, physical body, until the discovery of the atom and par ...
or
energy In physics, energy (from Ancient Greek: wikt:ἐνέργεια#Ancient_Greek, ἐνέργεια, ''enérgeia'', “activity”) is the physical quantity, quantitative physical property, property that is #Energy transfer, transferred to a phy ...
or
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
between a
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expres ...
and its surroundings. In 1824 Sadi Carnot described a thermodynamic system as the working substance (such as the volume of steam) of any heat engine under study.

# Overview

Thermodynamic equilibrium is characterized by absence of flow of mass or energy. Equilibrium thermodynamics, as a subject in physics, considers macroscopic bodies of matter and energy in states of internal thermodynamic equilibrium. It uses the concept of
thermodynamic process Classical thermodynamics considers three main kinds of thermodynamic process: (1) changes in a system, (2) cycles in a system, and (3) flow processes. (1)A Thermodynamic process is a process in which the thermodynamic state of a system is change ...
es, by which bodies pass from one equilibrium state to another by transfer of matter and energy between them. The term 'thermodynamic system' is used to refer to bodies of matter and energy in the special context of thermodynamics. The possible equilibria between bodies are determined by the physical properties of the walls that separate the bodies. Equilibrium thermodynamics in general does not measure time. Equilibrium thermodynamics is a relatively simple and well settled subject. One reason for this is the existence of a well defined physical quantity called 'the entropy of a body'. Non-equilibrium thermodynamics, as a subject in physics, considers bodies of matter and energy that are not in states of internal thermodynamic equilibrium, but are usually participating in processes of transfer that are slow enough to allow description in terms of quantities that are closely related to thermodynamic state variables. It is characterized by presence of flows of matter and energy. For this topic, very often the bodies considered have smooth spatial inhomogeneities, so that spatial gradients, for example a temperature gradient, are well enough defined. Thus the description of non-equilibrium thermodynamic systems is a field theory, more complicated than the theory of equilibrium thermodynamics. Non-equilibrium thermodynamics is a growing subject, not an established edifice. In general, it is not possible to find an exactly defined entropy for non-equilibrium problems. For many non-equilibrium thermodynamical problems, an approximately defined quantity called 'time rate of entropy production' is very useful. Non-equilibrium thermodynamics is mostly beyond the scope of the present article. Another kind of thermodynamic system is considered in engineering. It takes part in a flow process. The account is in terms that approximate, well enough in practice in many cases, equilibrium thermodynamical concepts. This is mostly beyond the scope of the present article, and is set out in other articles, for example the article
Flow process The region of space enclosed by open system boundaries is usually called a control volume. It may or may not correspond to physical walls. It is convenient to define the shape of the control volume so that all flow of matter, in or out, occurs ...
.

# History

The first to create the concept of a thermodynamic system was the French physicist Sadi Carnot whose 1824 ''
Reflections on the Motive Power of Fire ''Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power'' is a book published in 1824 by French people, French physicist Nicolas Léonard Sadi Carnot, Sadi Carnot.full text of 1897 ed. ( s:Reflections on the Motive ...
'' studied what he called the ''working substance'', e.g., typically a body of water vapor, in
steam engine A steam engine is a heat engine that performs mechanical work using steam as its working fluid. The steam engine uses the force produced by steam pressure to push a piston back and forth inside a Cylinder (locomotive), cylinder. This pus ...
s, in regards to the system's ability to do work when heat is applied to it. The working substance could be put in contact with either a heat reservoir (a boiler), a cold reservoir (a stream of cold water), or a piston (to which the working body could do work by pushing on it). In 1850, the German physicist
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Nicolas Léonard Sadi Ca ...
generalized this picture to include the concept of the surroundings, and began referring to the system as a "working body". In his 1850 paper ''On the Motive Power of Heat'', Clausius wrote: The article
Carnot heat engine A Carnot heat engine is a heat engine that operates on the Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded by Benoît Paul Émile Clapeyron in 1 ...
shows the original piston-and-cylinder diagram used by Carnot in discussing his ideal engine; below, we see the Carnot engine as is typically modeled in current use: In the diagram shown, the "working body" (system), a term introduced by Clausius in 1850, can be any fluid or vapor body through which
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
''Q'' can be introduced or transmitted through to produce work. In 1824, Sadi Carnot, in his famous paper ''Reflections on the Motive Power of Fire'', had postulated that the fluid body could be any substance capable of expansion, such as vapor of water, vapor of alcohol, vapor of mercury, a permanent gas, or air, etc. Though, in these early years, engines came in a number of configurations, typically ''QH'' was supplied by a boiler, wherein water boiled over a furnace; ''QC'' was typically a stream of cold flowing water in the form of a condenser located on a separate part of the engine. The output work ''W'' was the movement of the piston as it turned a crank-arm, which typically turned a pulley to lift water out of flooded salt mines. Carnot defined work as "weight lifted through a height".

# Systems in equilibrium

At
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal State variables, state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than systems not in equilibrium. In some cases, when analyzing a
thermodynamic process Classical thermodynamics considers three main kinds of thermodynamic process: (1) changes in a system, (2) cycles in a system, and (3) flow processes. (1)A Thermodynamic process is a process in which the thermodynamic state of a system is change ...
, one can assume that each intermediate state in the process is at equilibrium. This considerably simplifies the analysis. In isolated systems it is consistently observed that as time goes on internal rearrangements diminish and stable conditions are approached. Pressures and temperatures tend to equalize, and matter arranges itself into one or a few relatively homogeneous phases. A system in which all processes of change have gone practically to completion is considered in a state of
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal State variables, state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
. The thermodynamic properties of a system in equilibrium are unchanging in time. Equilibrium system states are much easier to describe in a deterministic manner than non-equilibrium states. For a process to be reversible, each step in the process must be reversible. For a step in a process to be reversible, the system must be in equilibrium throughout the step. That ideal cannot be accomplished in practice because no step can be taken without perturbing the system from equilibrium, but the ideal can be approached by making changes slowly.

# Walls

A system is enclosed by walls that bound it and connect it to its surroundings.Tisza, L. (1966), pp. 109, 112. Callen, H.B. (1960/1985), pp. 15, 17. Often a wall restricts passage across it by some form of matter or energy, making the connection indirect. Sometimes a wall is no more than an imaginary two-dimensional closed surface through which the connection to the surroundings is direct. A wall can be fixed (e.g. a constant volume reactor) or moveable (e.g. a piston). For example, in a reciprocating engine, a fixed wall means the piston is locked at its position; then, a constant volume process may occur. In that same engine, a piston may be unlocked and allowed to move in and out. Ideally, a wall may be declared adiabatic, diathermal, impermeable, permeable, or semi-permeable. Actual physical materials that provide walls with such idealized properties are not always readily available. The system is delimited by walls or boundaries, either actual or notional, across which conserved (such as matter and energy) or unconserved (such as entropy) quantities can pass into and out of the system. The space outside the thermodynamic system is known as the ''surroundings'', a ''reservoir'', or the ''environment''. The properties of the walls determine what transfers can occur. A wall that allows transfer of a quantity is said to be permeable to it, and a thermodynamic system is classified by the permeabilities of its several walls. A transfer between system and surroundings can arise by contact, such as conduction of heat, or by long-range forces such as an electric field in the surroundings. A system with walls that prevent all transfers is said to be isolated. This is an idealized conception, because in practice some transfer is always possible, for example by gravitational forces. It is an axiom of thermodynamics that an isolated system eventually reaches internal
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal State variables, state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
, when its state no longer changes with time. The walls of a
closed system A closed system is a natural physical system that does not allow transfer of matter in or out of the system, although — in contexts such as physics, chemistry or engineering — the transfer of energy (''e.g.'' as work or heat) is allowed. In ...
allow transfer of energy as heat and as work, but not of matter, between it and its surroundings. The walls of an ''open system'' allow transfer both of matter and of energy. This scheme of definition of terms is not uniformly used, though it is convenient for some purposes. In particular, some writers use 'closed system' where 'isolated system' is here used. Anything that passes across the boundary and effects a change in the contents of the system must be accounted for in an appropriate balance equation. The volume can be the region surrounding a single atom resonating energy, such as
Max Planck Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a Germans, German theoretical physicist whose discovery of quantum mechanics, energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial con ...
defined in 1900; it can be a body of steam or air in a
steam engine A steam engine is a heat engine that performs mechanical work using steam as its working fluid. The steam engine uses the force produced by steam pressure to push a piston back and forth inside a Cylinder (locomotive), cylinder. This pus ...
, such as Sadi Carnot defined in 1824. It could also be just one nuclide (i.e. a system of
quarks A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
) as hypothesized in quantum thermodynamics.

# Surroundings

The system is the part of the universe being studied, while the ''surroundings'' is the remainder of the universe that lies outside the boundaries of the system. It is also known as the ''environment'' or the ''reservoir''. Depending on the type of system, it may interact with the system by exchanging mass, energy (including heat and work),
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the Multiplication, product of the mass and velocity of an object. It is a Euclidean vector, vector quantity, possessing a magnitude and a dire ...
,
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electron ...
, or other conserved properties. The environment is ignored in the analysis of the system, except in regards to these interactions.

# Closed system

In a closed system, no mass may be transferred in or out of the system boundaries. The system always contains the same amount of matter, but (sensible) heat and (boundary) work can be exchanged across the boundary of the system. Whether a system can exchange heat, work, or both is dependent on the property of its boundary. * Adiabatic boundary – not allowing any heat exchange: A thermally isolated system * Rigid boundary – not allowing exchange of work: A mechanically isolated system One example is fluid being compressed by a piston in a cylinder. Another example of a closed system is a bomb calorimeter, a type of constant-volume calorimeter used in measuring the heat of combustion of a particular reaction. Electrical energy travels across the boundary to produce a spark between the electrodes and initiates combustion. Heat transfer occurs across the boundary after combustion but no mass transfer takes place either way. The first law of thermodynamics for energy transfers for closed system may be stated: :$\Delta U=Q-W$ where $U$denotes the internal energy of the system, $Q$ heat added to the system, $W$ the work done by the system. For infinitesimal changes the first law for closed systems may stated: :$\mathrm d U= \delta Q -\delta W.$ If the work is due to a volume expansion by $\mathrm d V$ at a pressure $P$ then: :$\delta W = P\mathrm d V.$ For a quasi-reversible heat transfer, the second law of thermodynamics reads: :$\delta Q = T \mathrm d S$ where $T$ denotes the thermodynamic temperature and $S$ the entropy of the system. With these relations the fundamental thermodynamic relation, used to compute changes in internal energy, is expressed as: :$\mathrm d U=T\mathrm d S-P\mathrm d V.$ For a simple system, with only one type of particle (atom or molecule), a closed system amounts to a constant number of particles. For systems undergoing a
chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
, there may be all sorts of molecules being generated and destroyed by the reaction process. In this case, the fact that the system is closed is expressed by stating that the total number of each elemental atom is conserved, no matter what kind of molecule it may be a part of. Mathematically: :$\sum_^m a_N_j=b_i^0$ where $N_j$ denotes the number of $j$-type molecules, $a_$ the number of atoms of element $i$ in molecule $j$, and $b_i^0$ the total number of atoms of element $i$ in the system, which remains constant, since the system is closed. There is one such equation for each element in the system.

# Isolated system

An isolated system is more restrictive than a closed system as it does not interact with its surroundings in any way. Mass and energy remains constant within the system, and no energy or mass transfer takes place across the boundary. As time passes in an isolated system, internal differences in the system tend to even out and pressures and temperatures tend to equalize, as do density differences. A system in which all equalizing processes have gone practically to completion is in a state of
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal State variables, state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
. Truly isolated physical systems do not exist in reality (except perhaps for the universe as a whole), because, for example, there is always gravity between a system with mass and masses elsewhere. However, real systems may behave nearly as an isolated system for finite (possibly very long) times. The concept of an isolated system can serve as a useful
model A model is an informative representation of an object, person or system. The term originally denoted the Plan_(drawing), plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a mea ...
approximating many real-world situations. It is an acceptable idealization used in constructing
mathematical model A mathematical model is a description of a system using mathematical concepts and language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languag ...
s of certain natural phenomena. In the attempt to justify the postulate of
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
increase in the
second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...
, Boltzmann's
H-theorem In classical statistical mechanics, the ''H''-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency to decrease in the quantity ''H'' (defined below) in a nearly-ideal gas of molecules. L. Boltzmann,Weitere Studien über das Wä ...
used equations, which assumed that a system (for example, a gas) was isolated. That is all the mechanical degrees of freedom could be specified, treating the walls simply as
mirror A mirror or looking glass is an object that Reflection (physics), reflects an image. Light that bounces off a mirror will show an image of whatever is in front of it, when focused through the lens of the eye or a camera. Mirrors reverse the ...
boundary conditions. This inevitably led to Loschmidt's paradox. However, if the
stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themsel ...
behavior of the
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
s in actual walls is considered, along with the
random In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no :wikt:order, order and does not follow an intelligible pattern or combination. Ind ...
izing effect of the ambient, background
thermal radiation Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
, Boltzmann's assumption of molecular chaos can be justified. The second law of thermodynamics for isolated systems states that the entropy of an isolated system not in equilibrium tends to increase over time, approaching maximum value at equilibrium. Overall, in an isolated system, the internal energy is constant and the entropy can never decrease. A ''closed'' system's entropy can decrease e.g. when heat is extracted from the system. It is important to note that isolated systems are not equivalent to closed systems. Closed systems cannot exchange matter with the surroundings, but can exchange energy. Isolated systems can exchange neither matter nor energy with their surroundings, and as such are only theoretical and do not exist in reality (except, possibly, the entire universe). It is worth noting that 'closed system' is often used in thermodynamics discussions when 'isolated system' would be correct – i.e. there is an assumption that energy does not enter or leave the system.

# Selective transfer of matter

For a thermodynamic process, the precise physical properties of the walls and surroundings of the system are important, because they determine the possible processes. An open system has one or several walls that allow transfer of matter. To account for the internal energy of the open system, this requires energy transfer terms in addition to those for heat and work. It also leads to the idea of the
chemical potential In thermodynamics, the chemical potential of a Chemical specie, species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potent ...
. A wall selectively permeable only to a pure substance can put the system in diffusive contact with a reservoir of that pure substance in the surroundings. Then a process is possible in which that pure substance is transferred between system and surroundings. Also, across that wall a contact equilibrium with respect to that substance is possible. By suitable thermodynamic operations, the pure substance reservoir can be dealt with as a closed system. Its internal energy and its entropy can be determined as functions of its temperature, pressure, and mole number. A thermodynamic operation can render impermeable to matter all system walls other than the contact equilibrium wall for that substance. This allows the definition of an intensive state variable, with respect to a reference state of the surroundings, for that substance. The intensive variable is called the chemical potential; for component substance it is usually denoted . The corresponding extensive variable can be the number of moles of the component substance in the system. For a contact equilibrium across a wall permeable to a substance, the chemical potentials of the substance must be same on either side of the wall. This is part of the nature of thermodynamic equilibrium, and may be regarded as related to the zeroth law of thermodynamics.

# Open system

In an open system, there is an exchange of energy and matter between the system and the surroundings. The presence of reactants in an open beaker is an example of an open system. Here the boundary is an imaginary surface enclosing the beaker and reactants. It is named ''closed'', if borders are impenetrable for substance, but allow transit of energy in the form of heat, and ''isolated'', if there is no exchange of heat and substances. The open system cannot exist in the equilibrium state. To describe deviation of the thermodynamic system from equilibrium, in addition to constitutive variables that was described above, a set of internal variables $\xi_1, \xi_2,\ldots$ that are called ''internal variables'' have been introduced. The equilibrium state is considered to be stable and the main property of the internal variables, as measures of non-equilibrium of the system, is their trending to disappear; the local law of disappearing can be written as relaxation equation for each internal variable where $\tau_i= \tau_i\left(T, x_1, x_2, \ldots, x_n\right)$ is a relaxation time of a corresponding variables. It is convenient to consider the initial value $\xi_i^0$ are equal to zero. The specific contribution to the thermodynamics of open non-equilibrium systems was made by Ilya Prigogine, who investigated a system of chemically reacting substances. In this case the internal variables appear to be measures of incompleteness of chemical reactions, that is measures of how much the considered system with chemical reactions is out of equilibrium. The theory can be generalized, to consider any deviations from the equilibrium state, such as structure of the system, gradients of temperature, difference of concentrations of substances and so on, to say nothing of degrees of completeness of all chemical reactions, to be internal variables. The increments of
Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work (physics), work that may be performed by a closed system, thermodynamically closed system a ...
$G$ and
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
$S$ at $T=const$ and $p=const$ are determined as The stationary states of the system exists due to exchange of both thermal energy $\Delta Q_\alpha$ and a stream of particles. The sum of the last terms in the equations presents the total energy coming into the system with the stream of particles of substances $\Delta N_\alpha$ that can be positive or negative; the quantity $\mu_\alpha$ is
chemical potential In thermodynamics, the chemical potential of a Chemical specie, species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potent ...
of substance $\alpha$. The middle terms in equations (2) and (3) depicts energy dissipation (
entropy production Entropy production (or generation) is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes including motion of bodies, heat exchange, fluid flow, substances expanding or mixing, Anelasticity ...
) due to the relaxation of internal variables $\xi_j$, while $\Xi_$ are thermodynamic forces. This approach to the open system allow describing the growth and development of living objects in thermodynamic terms.

*
Dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...
* Energy system *
Isolated system In Outline of physical science, physical science, an isolated system is either of the following: # a physical system so far removed from other systems that it does not interact with them. # a thermodynamic system enclosed by rigid immovable T ...
*
Mechanical system A machine is a physical system using Power (physics), power to apply Force, forces and control Motion, movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to na ...
*
Physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment (systems), environment. The environment is ignored except ...
*
Quantum system Quantum mechanics is a fundamental Scientific theory, theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including qua ...
*
Thermodynamic cycle A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventu ...
*
Thermodynamic process Classical thermodynamics considers three main kinds of thermodynamic process: (1) changes in a system, (2) cycles in a system, and (3) flow processes. (1)A Thermodynamic process is a process in which the thermodynamic state of a system is change ...
* Two-state quantum system

# Sources

* * Callen, H.B. (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, . * * {{Thermodynamic cycles, state=collapsed Thermodynamic systems Equilibrium chemistry Thermodynamic cycles Thermodynamic processes