Philosophy of thermal and statistical physics
Encyclopedia
The philosophy of thermal and statistical physics is that part of the philosophy of physics
whose subject matter is classical thermodynamics
, statistical mechanics
, and related theories. Its central questions include: What is entropy
, and what does the second law of thermodynamics say about it? Does either thermodynamics or statistical mechanics contain an element of time
-irreversibility? If so, what does statistical mechanics tell us about the arrow of time
?
behaviour of physical systems under the influence of exchange of work
and heat
with other systems or their environment. It is not concerned with the microscopic properties of these systems, such as the movements of atom
s.
At the very heart of contemporary thermodynamics lies the idea of thermodynamic equilibrium
, a state in which no macroscopic properties of the system change over time. In orthodox versions of thermodynamics, properties such as temperature
and entropy
are defined for equilibrium states only. The assertion that all thermodynamic systems occupying a fixed volume will reach equilibrium in infinite time, which has been central but tacit to thermodynamics, has recently been dubbed the "minus first law of thermodynamics."
. There is a fourth law
, not discussed here.
when 1) both of the systems are in equilibrium, and 2) they remain in equilibrium when they are brought into contact, where 'contact' is meant to imply the possibility of exchanging heat, but not work or particles. Thermal equilibrium is:
Hence thermal equilibrium
between systems is an equivalence relation
, and this is the substance of the zeroth law of thermodynamics
. According to Max Planck
, who wrote an influential textbook on thermodynamics, and many other authors, this empirical principle shows that we can define the "temperature function" central to our everyday conception of heat.
The understanding of the First Law embodied in classical physics
can be summarized by the saying: "Energy can be neither created nor destroyed."
Because of the:
the above classical version of the First Law must be amended as follows:
"The total energy of the universe, including the energy equivalent of all baryon
s, boson
s, and lepton
s in the universe, is constant for all time."
is given (is allowed to occupy) new energy states
which are equivalent to the existing states (say, a gas is expanding into a larger volume), then the system will occupy "new" states on equal footing with the existing ("old") ones. This is the central postulate of statistical mechanics
- that equivalent energy states cannot be distinguished. Thus, as the number of energy states increases, the energy of the system will be spread among more and more states, thereby increasing the entropy
of the system.
The Second Law can be summarized by either of the following sayings:
Some wags have proposed the following summary of the First and Second Laws: "The first law says you can't win, the second law says you can't even break even."
There are various interpretations of the Second Law, one being Boltzmann's
H-theorem
.
, in an 1871 essay titled the "Theory of Heat," proposed a thought experiment
showing why the Second Law might just be a temporary condition, why entropy might be beatable. This thought experiment came to be called Maxwell's Demon
.
He went on to explain that the demon working at a microscopic level, could operate a gate (presumably of low-friction construction) allowing only swift molecules to pass through it. In this way, the demon's work would result in slow molecules (i.e. cold) on one side of the gated barrier, and heat on the other side. Yet movement from uniformity of temperature to a split of hot/cold violates the Second Law. It follows, Maxwell thought that the Second Law was just a provisional consequence of technological limitations that would be eventually overcome when humans would be capable of observing and manipulating individual molecule
s.
In the 20th century, advances in information theory
and thermodynamics eventually showed how the proverbial demon's measuring and manipulating activities would necessarily increase total entropy by more than his actions decreased the entropy of the closed gaseous system. Hence Maxwell's demon could not decrease total entropy
even in principle, and Maxwell's proposed exception to the Second Law stands refuted.
Philosophy of physics
In philosophy, the philosophy of physics studies the fundamental philosophical questions underlying modern physics, the study of matter and energy and how they interact. The philosophy of physics begins by reflecting on the basic metaphysical and epistemological questions posed by physics:...
whose subject matter is classical thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
, and related theories. Its central questions include: What is entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
, and what does the second law of thermodynamics say about it? Does either thermodynamics or statistical mechanics contain an element of time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
-irreversibility? If so, what does statistical mechanics tell us about the arrow of time
Arrow of time
The arrow of time, or time’s arrow, is a term coined in 1927 by the British astronomer Arthur Eddington to describe the "one-way direction" or "asymmetry" of time...
?
What is thermodynamics?
Thermodynamics is the study of the macroscopicMacroscopic
The macroscopic scale is the length scale on which objects or processes are of a size which is measurable and observable by the naked eye.When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences or...
behaviour of physical systems under the influence of exchange of work
Work (thermodynamics)
In thermodynamics, work performed by a system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system. As such, thermodynamic work is a generalization of the concept of mechanical work in mechanics. Thermodynamic work encompasses...
and heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
with other systems or their environment. It is not concerned with the microscopic properties of these systems, such as the movements of atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s.
At the very heart of contemporary thermodynamics lies the idea of thermodynamic equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...
, a state in which no macroscopic properties of the system change over time. In orthodox versions of thermodynamics, properties such as temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
and entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
are defined for equilibrium states only. The assertion that all thermodynamic systems occupying a fixed volume will reach equilibrium in infinite time, which has been central but tacit to thermodynamics, has recently been dubbed the "minus first law of thermodynamics."
The laws of thermodynamics
Traditionally, thermodynamics has often been described as a "theory of principle." This is a theory in which a few empirical generalisations are taken for granted, and from them the rest of the theory is deduced. According to this view, there is a strong correspondence between three empirical facts and the first three laws of thermodynamicsThermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
. There is a fourth law
Onsager reciprocal relations
In thermodynamics, the Onsager reciprocal relations express the equality of certain ratios between flows and forces in thermodynamic systems out of equilibrium, but where a notion of local equilibrium exists....
, not discussed here.
The zeroth law
Two systems are said to be in thermal equilibriumThermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...
when 1) both of the systems are in equilibrium, and 2) they remain in equilibrium when they are brought into contact, where 'contact' is meant to imply the possibility of exchanging heat, but not work or particles. Thermal equilibrium is:
- ReflexiveReflexiveReflexive may refer to:In fiction:*MetafictionIn grammar:*Reflexive pronoun, a pronoun with a reflexive relationship with its self-identical antecedent*Reflexive verb, where a semantic agent and patient are the same...
: Any system is in thermal equilibrium with itself; - Symmetric: if system A is in thermal equilibrium with system B, then it is also the case that B is in equilibrium with A;
- Transitive: It is an empirical fact that if system A is in thermal equilibrium with system B, and system B is in thermal equilibrium with system C, then system A and system C are also in thermal equilibrium.
Hence thermal equilibrium
Thermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...
between systems is an equivalence relation
Equivalence relation
In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition. Two elements of the set are considered equivalent if and only if they are elements of the same cell...
, and this is the substance of the zeroth law of thermodynamics
Zeroth law of thermodynamics
The zeroth law of thermodynamics is a generalization principle of thermal equilibrium among bodies, or thermodynamic systems, in contact.The zeroth law states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.Systems are said to...
. According to Max Planck
Max Planck
Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...
, who wrote an influential textbook on thermodynamics, and many other authors, this empirical principle shows that we can define the "temperature function" central to our everyday conception of heat.
The first law
In simplest terms, the First Law states that the internal energy level of an isolated system is a constant. In the context of a non-isolated system, this law requires that when there is a change in energy when going from one equilibrium state to another, that change is equal to the heat transfer into the system minus the work done by the system. Hence energy in minus energy out equals the change in energy.The understanding of the First Law embodied in classical physics
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...
can be summarized by the saying: "Energy can be neither created nor destroyed."
Because of the:
- Mass-energy equivalenceMass-energy equivalenceIn physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept, mass is a property of all energy, and energy is a property of all mass, and the two properties are connected by a constant...
that is a consequence of special relativitySpecial relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
(summarized by the famous equation E=mc2); - Standard ModelStandard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
of particle physicsParticle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
; - Spontaneous emergence of elementary particleElementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s out of the vacuumVacuumIn everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...
, as explained by quantum theoryQuantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, and the equally spontaneous decay of single particles and the mutual annihilation of particles and anti-particles,
the above classical version of the First Law must be amended as follows:
"The total energy of the universe, including the energy equivalent of all baryon
Baryon
A baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...
s, boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
s, and lepton
Lepton
A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
s in the universe, is constant for all time."
The second law of thermodynamics
In a general sense, the Second Law says that temperature differences between systems in contact with each other tend to even out and that work can be obtained from these non-equilibrium differences, but that loss of heat occurs in the form of entropy when work is done. This law follows simply from statistics: if a physical systemPhysical system
In physics, the word system has a technical meaning, namely, it is the portion of the physical universe chosen for analysis. Everything outside the system is known as the environment, which in analysis is ignored except for its effects on the system. The cut between system and the world is a free...
is given (is allowed to occupy) new energy states
Thermodynamic state
A thermodynamic state is a set of values of properties of a thermodynamic system that must be specified to reproduce the system. The individual parameters are known as state variables, state parameters or thermodynamic variables. Once a sufficient set of thermodynamic variables have been...
which are equivalent to the existing states (say, a gas is expanding into a larger volume), then the system will occupy "new" states on equal footing with the existing ("old") ones. This is the central postulate of statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
- that equivalent energy states cannot be distinguished. Thus, as the number of energy states increases, the energy of the system will be spread among more and more states, thereby increasing the entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
of the system.
The Second Law can be summarized by either of the following sayings:
- "The entropy of any closed thermodynamic systemThermodynamic systemA thermodynamic system is a precisely defined macroscopic region of the universe, often called a physical system, that is studied using the principles of thermodynamics....
cannot decrease." - "The entropy of the universeUniverseThe Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
cannot decrease."
Some wags have proposed the following summary of the First and Second Laws: "The first law says you can't win, the second law says you can't even break even."
There are various interpretations of the Second Law, one being Boltzmann's
Ludwig Boltzmann
Ludwig Eduard Boltzmann was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics...
H-theorem
H-theorem
In Classical Statistical Mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the increase in the entropy of an ideal gas in an irreversible process. H-theorem follows from considerations of Boltzmann's equation...
.
Maxwell's Demon
James Clerk MaxwellJames Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
, in an 1871 essay titled the "Theory of Heat," proposed a thought experiment
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...
showing why the Second Law might just be a temporary condition, why entropy might be beatable. This thought experiment came to be called Maxwell's Demon
Maxwell's demon
In the philosophy of thermal and statistical physics, Maxwell's demon is a thought experiment created by the Scottish physicist James Clerk Maxwell to "show that the Second Law of Thermodynamics has only a statistical certainty." It demonstrates Maxwell's point by hypothetically describing how to...
.
- "If we conceive a being whose faculties are so sharpened that he can follow every moleculeMoleculeA molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
in its course, such a being, whose attributes are still essentially finite as our own, would be able to do what is at present impossible for us," (J. C. Maxwell)
He went on to explain that the demon working at a microscopic level, could operate a gate (presumably of low-friction construction) allowing only swift molecules to pass through it. In this way, the demon's work would result in slow molecules (i.e. cold) on one side of the gated barrier, and heat on the other side. Yet movement from uniformity of temperature to a split of hot/cold violates the Second Law. It follows, Maxwell thought that the Second Law was just a provisional consequence of technological limitations that would be eventually overcome when humans would be capable of observing and manipulating individual molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
s.
In the 20th century, advances in information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
and thermodynamics eventually showed how the proverbial demon's measuring and manipulating activities would necessarily increase total entropy by more than his actions decreased the entropy of the closed gaseous system. Hence Maxwell's demon could not decrease total entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
even in principle, and Maxwell's proposed exception to the Second Law stands refuted.
External links
- Stanford Encyclopedia of PhilosophyStanford Encyclopedia of PhilosophyThe Stanford Encyclopedia of Philosophy is a freely-accessible online encyclopedia of philosophy maintained by Stanford University. Each entry is written and maintained by an expert in the field, including professors from over 65 academic institutions worldwide...
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