IoHT :: 110+ Variations of the Second Law of Thermodynamics

Pick the best 2nd Law:
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[1] Hippocrates (c. 440 BC). NEED SOURCE [email me if you have it]

[2] Lavoisier, A. (1789). Memoir by Armand Seguin and Antonine Lavoisier, dated 1789, quoted in Laviosier, A. (1862). Oeuvres de Lavoisier, Paris: Imprimereie Imperiale.

[3-4] Carnot, S. (1824). Reflections on the Motive Power of Fire and on the Machines Fitted to Develop that Power. Paris: Chex Bachelier, Libraire. [PDF].

[5-8] Clausius, R. (1850). Monograph: Uber die bewegende Kraft der Warme. See: Mechanical Theory of Heat by R. Clausius (Nine memoirs on the development of the Concept of Entropy) [1850-65]; [URL]

[9] Kelvin, L. (1852). NEED SOURCE [email me if you have it]

[10] Kelvin, L. (1852). Source: Kelvin "Quotations" Website [URL] + "On the Dynamical Theory of Heat" [URL].

[11] Kelvin, L. (1852). Source: Kelvin "Quotations" Website [URL] + Proceedings of the Royal Society of Edinburgh, vol. 3, 139, 1852, "On a Universal Tendency in Nature to the Dissipation of Mechanical Energy"

[12] Kelvin, L. (1852). Source: Kelvin "Quotations" Website [URL] + See footnotes in: "On a Universal Tendency in Nature to the Dissipation of Mechanical Energy, [URL]" Proceedings of the Royal Society of Edinburgh, April 19, 1852; or the Philosophical Magazine, October, 1852; also Mathematical and Physical Papers, vol. i, art. 59.

[13] Kelvin, L. (1852). Source: Kelvin "Quotations" Website [URL] + See "On a Universal Tendency in Nature to the Dissipation of Mechanical Energy," Proceedings of the Royal Society of Edinburgh, April 19, 1852; or

the Philosophical Magazine, October, 1852; also Mathematical and Physical Papers, vol. i, art. 59. Also: "On a Universal Tendency" [URL]

[14] Clausius, R. (1865). Source: Bent, H. (1965). The Second Law – an Introduction to Classical and Statistical Thermodynamics. (textbook). New York: Oxford University Press. See: Mechanical Theory of Heat by R. Clausius (Nine memoirs on the development of the Concept of Entropy) [1850-65]; [URL]

[15] Kelvin & Planck. (1879). NEED SOURCE [email me if you have it]

[16-17] Planck. M. (1897). Treatise on Thermodynamics (texbook). New York: Dover Publications, Inc.

[18] Caratheodory, C. (1908). Investigations into the Foundations of Thermodynamics. [in: Kestin, J. (1976). The Second Law of Thermodynamics, Bench Mark Papers on Energy; vol. 5. pp 229-56. New York: Dowden, Hutchinson, and Ross.]

[19-21] Fermi, E. (1936). Thermodynamics. New York: Dover Publications, Inc.

[22-23] Bridgman, P. (1941). The Nature of Thermodynamics (textbook). New York: Harper & Brothers.

[24] Keenan, J. (1941). Thermodynamics (textbook). New York: John Wiley & Sons.

[25-26] Klotz. I. (1950). Chemical Thermodynamics (textbook). New York: Prentice Hall. Inc.

[27] Fritz, A. (1959). Thermodynamics and Statistical Thermodynamics (textbook). New York: John Wiley & Sons, Inc.

[28] King, A. (1962). Thermophysics (textbook). San Francisco: W.H. Freeman & Company.

[29-30] Lee, J. & Sears, F. (1963). Thermodynamics – an Introductory Text for Engineering Students. London: Addison-Wesley Publishing Company, Inc.

[31-32] Bazarov, I. (1964). Thermodynamics (textbook). New York: The Macmillan Company.

[33] Bent, H. (1965). The Second Law – an Introduction to Classical and Statistical Thermodynamics. (textbook). New York: Oxford University Press.

[34] Hatsopoulos, G. & Keenan, J. (1965). Principles of General Thermodynamics. New York: John Wiley.; Kestin, J. (1968). A Course in Thermodynamics. New York: Hemisphere Press.

[35-37] Kern, R. & Weisbrod, A. (1967). Thermodynamics for Geologists (textbook). San Francisco: Freeman, Cooper and Company.

[38] Battino, R. & Wood, S. (1968). Thermodynamics an Introduction. (textbook). New York: Academic Press.

[39] Bekenstein, J. (1971). Source: von Baeyer, H. C. (2004). Information - the New Language of Science. Massachusetts: Harvard University Press.

[40-41] Lehninger, A. (1971). Bioenergetics - the Molecular Basis of Biological Energy Transformations, 2nd. Ed. London: The Benjamin/Cummings Publishing Company.

[42] Prigogine, I. (1977). Nobel Lecture: Time, Structure and Flucturations. [PDF]

[43-44] Adkins, C. (1983). Equilibrium Thermodynamics, 3rd Ed. (textbook). Cambridge: Cambridge University Press.

[45-52] Atkins, P. (1984). The Second Law. New York: Scientific American Books.

[53] Groot, de S.R. & Mazur, P. (1984). Non-Equilibrium Thermodynamics (textbook). New York: Dover Publications, Inc.

[54] Barrow, G. (1988). Physical Chemistry, 5th Ed. (textbook). New York: McGraw Hill, Inc.

[55-56] Halliday, D. & Resnick, R. (1988). Fundamentals of Physics, 3rd Ed. (textbook). New York: John Wiley & Sons.

[57] Serway, R. (1990). Physics for Scientists & Engineers, 3rd Ed. (textbook). Chicago: Saunders College Publishing.

[58] Ebbing (1990). NEED SOURCE [email me if you have it]

[59] Schneider, E. & Kay, J. (1991). Life as a Manifestation of the Second Law of Thermodynamics [HTML]

[60] Rosen, R. (1991) Life Itself: A Comprehensive Inquirey Into the Nature, Origin and Fabrication of Life. New York: Columbia University Press. (pg. 114). [URL] (excerpt).

[61] Lehninger, A., Nelson, D., & Cox, M. (1993). Principles of Biochemistry, 2nd Ed (textbook). New York: Worth Publishers.

[62] Schneider, E. & Kay, J. (1995). Order from Disorder: the Thermodynamics of Complexity. [URL]

[63-65] Black, W. & Hartley, J. (1996). Thermodynamics, 3rd Ed. (textbook). New York: Harper Collins.

[66] Gleick, J. (1997). Chaos - Making of New Science. New York: Penguin Books.

[67-68] Nordholm, S. (1997). "In Defense of Thermodynamics - an Animate Analogy" [URL]. Journal of Chemical Education [JCE]. Vol. 74, No. 3, pg. 273.

[69-70] Prigogine, I. & Kondepudi, D.(1998). Modern Thermodynamics – From Heat Engines to Dissipative Structures (textbook). New York: John Wiley & Sons.

[71-73] Perrot, Pierre. (1998). A to Z of Thermodynamics (dictionary). New York: Oxford University Press.

[74] Chang, R. (1998). Chemisty, 6th. Ed. (textbook). New York: McGraw-Hill.

[75-76] Cutnell, J. & Johnson, K. (1998). Physics, 4th Ed. (textbook). New York: John Wiley & Sons, Inc.

[77] Baierlein, R. (1999). Thermal Physics (texbook). New York: Cambridge University Press.

[78] Swenson, R. (1999). Spontaneous Order, Evolution, and Natural Law. Center for the Ecological Study of Perception and Action Department of Psychology, University of Connecticut [URL (home); URL (2nd Law 'excerpt'), PDF (full 32-pg paper)].

[79-83] Wark, R. & Richards, D. (1999). Thermodynamics, 6th Ed. (textbook). New York: McGraw-Hill.

[84] Gribbon, J. (2000). Q is for Quantum: an Encyclopedia of Particle Physics. New York: Sion & Schuster.

[85-88] Schroeder, D. (2000). An Introduction to Thermal Physics. (textbook). New York: Addison Wesley Longman.

[89-94] Haynie, D. (2001). Biological Thermodynamics (textbook). Cambridge: Cambridge University Press.

[95] Kay, J. (2002). NEED SOURCE [email me if you have it]

[96] Cengel, Y. & Boles, M. (2002). Thermodynamics – an Engineering Approach, 4th Ed. (textbook). New York: McGraw Hill.

[97] Chin, J. (2002). Economic an biological evolution: a non-equilibrium thermodynamic theory. Canada: Thermo Link Research. [URL (website), PDF & HTML (22-pg article/abstract)

[98-99] Avery, J. (2003). Information Theory and Evolution. New Jersey: World Scientific.

[100] N/A

[101] Baeyer (2004). NEED SOURCE [email me if you have it]

[102] Gladyshev. G. (2004). The 2nd Law of Thermodynamics and Evolution of Living Systems. Moscow: N.N. Semenov Institute of Chemical Physics, RAS. [related link: URL]

[103-105] N/A

[106-107] Schneider, E. & Sagan, D. (2005). Into The Cool - Energy Flow, Thermodynamics, and Life. Chicago: University of Chicago Press.

[108-109] Thims, L. (2005/06). Human Thermodynamics, Vol I-III. Chicago: IoHT Publishing Ltd. [Book Store]

[110] Porteus, E. (2005). Journal of Human Thermodynamics [JHT], Vol 1. Issue, 3.: Life and the Second Law of Thermodynamics [URL]. Chicago: IoHT Publishing Ltd. + Porteus, E. (1987). My Twentieth Century Philosophy. New York: Carlton Press, Inc.

[111-112] Klyce, B. (2005). Cosmic Ancestry: 'The Second Law of Thermodynamics' [URL].

[113-116] Smith, J., Van Ness, H., & Abbott, M. (2005). Introduction to Chemical Engineering Thermodynamics, 6th Ed. (textbook). New York: McGraw Hill.

[117-118] Penrose, R. (2005). The Road to Reality - A Complete Guide to the Laws of the Universe. New York: Knopf [Random House, Inc.]

NOTE 2:

A reason why there are so many varieties of the second law is that heat, or energy in transit, and the varieties of work, technically weight lifted through a height, produced from such heat movements are by no means limited to mechanical engines. As it is currently understood there are four principle varieties of energy: gluons, photons, bosons, and gravitons. Thus, the concept that "the flow of energy moves from hot to cold" is a very general statement applicable to virtually all types of dynamics. For example, heat from the sun, i.e. photons, works to make sunflowers by lifting the weight of atoms and molecules, from the soil of which they originate, though a vertical height and into their structural configuration. Hence, a corollary of the second law of thermodynamics governs the ontogeny or lifecycle of organisms as well as the phylogeny or evolution of species of organisms. According to this reasoning, by logical extrapolation, there exist numerous 2nd Law variations, each applicable to its own relative system. By reduction, however, all such varieties have simply to do with the natural direction in which heat produces work or energy instills dynamics.

The Kelvin-Planck and Clausius statements are most frequently used in engineering thermodynamic courses. The Hatsopoulos-Keenan statement is most frequently used in the environmental sciences. That is, this statement postulates the existence of (stable) equilibrium natural states reached by systems, living or otherwise, subjected to specified constraints as internal partitions, external conservative force fields, rigid impermeable walls, etc. This statement implies that one particular equilibrium state will be reached. Thus, the approach to equilibrium is quite directional in nature.

NOTE 3:

For the sake of clarity, "entropy" may be defined, in its cleanest form, as:

Heat, a quantity which functions to animate, derives from an internal fire located in the left ventricle.

Hippocrates
[c. 460 BC]

…in general, respiration is a nothing but a slow combustion of carbon and hydrogen, which is entirely similar to that which occurs in a lighted lamp or candle, and that, from this point of view, animals that respire are true combustible bodies that burn and consume themselves… / …, this torch of Prometheus, does not only represent an ingenious and poetic idea, it is a faithful picture of the operations of nature, at least for animals that breathe; one may therefore say, with the ancients, that the torch of life lights itself at the moment the infant breathes for the first time, and it does not extinguish itself except at death.

Lavoisier
[1789]

The production of heat is not sufficient to give birth to the impelling power. It is necessary that there should be cold; without it, the heat would be useless.

Carnot
[1824]

The production of motive power in heat engines is due not to an actual consumption of the caloric, but to its transportation from a warm body to a cold body, that is, to its re-establishment of equilibrium.

Carnot
[1824]

The ratio of heat content of a closed system to its absolute temperature always increases in any process.

Clausius
[1850]

Heat cannot of itself pass from a colder to a hotter body.

Clausius
[1850]

It is impossible to transfer heat from a cold to a hot reservoir without at the same time converting a certain amount of work to heat.

Clausius
[1850]

The entropy of the world tends towards a maximum.

Clausius
[1850]

No cyclic process is possible whose sole result is a flow of heat from a single reservoir and the performance of equivalent work.

Kelvin
[1852]

10.

It is impossible by means of inanimate material agency to derive a mechanical effect from a portion of matter by cooling it below the temperature of the coldest surrounding bodies.

Kelvin
[1852]

11.

There is at present in the material world a universal tendency to the dissipation of mechanical energy.

Kelvin
[1852]

12.

Although mechanical energy is indestructible, there is a universal tendency to its dissipation, which produces throughout the system a gradual augmentation and diffusion of heat, cessation of motion and exhaustion of the potential energy of the material Universe.

Kelvin
[1852]

13.

Any restoration of mechanical energy, without more than an equivalent of dissipation, is impossible in inanimate material processes, and is probably never effected by means of organized matter, either endowed with vegetable life, or subjected to the will of an animated creature.

Kelvin
[1852]

14.

For any process the sum of all entropy changes occurring as a result of the process is greater than zero and approaches zero in the limit as the process becomes reversible.

Clausius
[1865]

15.

It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work.

Kelvin & Planck
[1879]

16.

Every physical or chemical process in nature takes place in such a way as to increase the sum of the entropies of all the bodies taking any part in the process. In the limit, i.e. for reversible processes, the sum of the entropies remains unchanged.

Planck
[1897]

17.

There exists in nature a quantity which changes always in the same sense in all natural processes.

Planck
[1897]

18.

In the neighborhood of any given state of any closed system, there exist states which are inaccessible from it, along any adiabatic path reversible or irreversible.

Caratheodory
[1908]

19.

A transformation whose only final result is to transform into work heat extracted from a source which is at the same temperature throughout is impossible.

Fermi
[1936]

20.

A transformation whose only final result is to transfer heat from a body at a given temperature to a body at a higher temperature is impossible.

Fermi
[1936]

21.

If heat flows by conduction from a body A to another body B, then a transformation whose only final result is to transfer heat from B to A is impossible.

Fermi
[1936]

22.

Isolated systems seek a dead level.

Bridgman
[1941]

23.

A perpetual motion machine of the second kind is impossible.

Keenan
[1941]

24.

It is impossible to construct an engine which will work in a complete cycle and produce no effect except to raise a weight and exchange heat with a single reservoir (Planck Formulation).

Keenan
[1941]

25.

It is impossible to construct a machine which is able to convey heat by a cyclical process from one reservoir at a lower temperature to another at a higher temperature unless work is done on the machine by some outside agency.

Koltz
[1950]

26.

It is impossible to take heat from a reservoir at constant temperature and convert it into work without accompanying changes in the reservoir or its surroundings.

Koltz
[1950]

27.

Any process whose only result is the conversion of heat into work at a constant temperature is an impossibility.

Fritz
[1959]

28.

No process exists whereby the only effect is either to convert heat from a single thermal reservoir at a positive temperature completely into work on a system, or to transform work on a system completely into heat and to deliver it to a single thermal reservoir at a negative temperature [Kelvin-Planck-Ramsey statement].

King
[1962]

29.

No cyclic process is possible whose result is the flow of heat from a single heat reservoir and the performance of an equivalent amount of work on a work reservoir [Kelvin-Planck statement].

Lee & Sears
[1963]

30.

No cyclic process is possible whose result is the flow of heat out of a heat reservoir at one temperature and the flow of an equal quantity of heat into a second reservoir at a higher temperature [Clausius statement].

Lee & Sears
[1963]

31.

A perpetual motor of the second kind is impossible and this statement admits no converse proposition.

Bazarov
[1964]

32.

The law of existence of entropy in every equilibrium system and of its never decreasing in isolated systems for any processes whatsoever.

Bazarov
[1964]

33.

The entropy of the universe tends to increase.

Bent
[1965]

34.

When an isolated system performs a process after the removal of a series of internal constraints, it will reach a unique state of equilibrium: this state of equilibrium is independent of the order in which the constraints are removed.

Hatsopoulos, Keenan & Kestin
[1968]

35.

It is a completely general fact of observation that in nature changes have a definite sense, some are spontaneous (natural), others not so (unnatural) [Planck terms].

Kern & Weisbrod
[1967]

36.

Two bodies which are at different temperatures exchange heat in such a manner that heat flows naturally from the hotter to the colder body.

Kern & Weisbrod
[1967]

37.

When a system evolves naturally, i.e. undergoes a natural process, in an isothermal manner, at constant volume or constant pressure, its Gibbs free energy [G] or Helmholtz free energy [F] always decreases:

T, V constant, ΔF < 0
T, P constant, ΔG < 0

"Criterion for Evolution"
[where: F = U – TS and G = H – TS]

Kern & Weisbrod
[1967]

38.

No isolated system can be returned to its original state when a natural cyclic process takes place in the system.

Battino & Wood
[1968]

39.

The sum of black hole entropy plus the sum of ordinary entropy never decreases.

Bekenstein
[1971]

40.

All spontaneous physical and chemical changes have a preferred direction which can be predicted using the equilibrium criterion for the given process.

Lehninger
[1971]

41.

All physical and chemical processes proceed in such a direction that the randomness or entropy of the universe (the system plus its surroundings) increases to the maximum possible at which point there is equilibrium.

Lehninger
[1971]

42.

In isolated systems exchanging neither energy nor matter with the outside world, their exists an inequality, dS/dt ≥ 0, which ascertains the existence of a function, the entropy S, which increases monotonically until it reaches its maximum at the state of thermodynamic equilibrium.

Prigogine
[1977]

43.

No process is possible whose sole result is the transfer of heat from a colder to a hotter body [Clausius statement].

Adkins
[1983]

44.

No process is possible whose sole result is the complete conversion of heat into work [Kelvin statement].

Adkins
[1983]

45.

No process is possible in which the sole result is the transfer of energy from a cooler to a hotter body [Clausius statement].

Atkins
[1984]

46.

No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work [Kelvin statement].

Atkins
[1984]

47.

Natural processes are accompanied by an increase in the entropy of the universe [Clausius-Kelvin statement].

Atkins
[1984]

48.

Energy tends to disperse.

Atkins
[1984]

49.

Coherence tends to collapse into incoherence.

Atkins
[1984]

50.

Kinetic motion tends to degrade or dissipate into thermal motion.

Atkins
[1984]

NOTE 4:

In essence, the second law deals with the natural bounds on the phenomenon of 'heat':

(A) heat flows in a preferred direction.

(B) there exists a limit as to amount of work derivable from such heat flow.

NOTE 5:

‘The second law has yet to reach its most potent all-inclusive form’

NOTE 6:

In the future, knowing that entropy and heat are not 'fundamental' entities, the second law will need to be refurbished into a more encompassing description of fundamental interactions, as based on the standard model. For example, in 2005 mathematician Roger Penrose states: “I do not see entropy as an ‘absolute’ notion in present-day physical theory. There is, however, the possibility that it might acquire a more fundamental status in the future. For this, quantum physics would certainly need to be taken into consideration [Penrose]." His consensus is such that in a deeper context where quantum-gravitational considerations become important, especially in relations to black-hole entropy, there may be a more fundamental status for this kind of notion. Two very tentative variations of "fundamental second laws" are listed above [Thims].

NOTE #7

Entropy and the 2nd Law are two of the most confused concepts going in current science. For example, in 1949 when Claude Shannon, an electrical engineer and the father of information theory, asked John von Neumann, a chemical engineer and the father of game theory, what he should call his "missing information" (from phone line signals), Neumann told him to call it 'entropy' because:

1. A mathematical development very much like yours already exists in Boltzmann's statistical mechanics.

2. No one understands entropy very well, so in any discussion you will be in a position of advantage.

Out of this slight error in judgment, one can go online today and find people presenting information theory entropy meaning of life articles, or information theory entropy evolution discussions, and so on; which are clearly things which have nothing to do with each other (i.e. phone line signals & evolution).

NOTE #8

When deciding as to which version of the 2nd Law to use, one must first determine the system type. A system is defined as the region of space under study. A boundary separates the system from the surroundings. Across this boundary only three things may pass: work, heat, or matter [Perrot]. As based on this framework, there are four dominant classes of systems:

(a) Isolated Systems – matter and energy may not cross the boundary.

(b) Adiabatic Systems – heat and matter may not cross the boundary.

(d) Open Systems – heat, work, and matter may cross the boundary.

The 2nd Law statements of the form: “a system’s entropy can only increase” belong to classes (a) and (b). Systems in classes (c) and (d) may actually undergo decreases of entropy due to passages of heat and / or matter across the boundary surface [Denbigh].

Denbigh, K. (1989). “A Chemical Engineer’s Discourse on Entropy, Disorder, and Disorganization”

Link: [http://endeav.org/evolut/text/denbig1/denbit1e.htm]

Generally, these numerous 2nd Law varieties may be divided into system type subject to the constraints:

TYPE 1: a system, with no external heat flux, set out of equilibrium

TYPE 2: a system, with external heat flux, set out of equilibrium.

In this manner, the majority of these atomic 2nd Law varieties may be divided accordingly:

VERSON #1: non-heat-fluxed molecules left to their own accord will disorganize.

VERSON #2: heat-fluxed molecules left to their own accord will organize.

Thus, in the human scheme of things, an abandoned house, i.e. a bunch of connected molecules, in some neighborhood, i.e. system, will follow version #1. Conversely, a kept-up house in a fancy neighborhood will follow version #2. Hence, there exist two separate tendencies depending upon the flow of heat, or energy in transit, across the system boundary.

51.

The driving force of chemical reactions.

Atkins
[1984]

52.

Although the total quantity of energy must be conserved in any process, the distribution of that energy changes in an irreversible manner; the second law is concerned with the natural direction of change of the distribution of energy.

Atkins
[1984]

53.

The differential of the entropy produced inside a system must be zero for reversible (or equilibrium) transformations and positive for irreversible transformations of the system.

Groot & Max
[1984]

54.

Any statement about the direction of spontaneous change.

Barrow
[1988]

55.

In any thermodynamic process that proceeds from one equilibrium state to another, the entropy of the system + environment either remains unchanged or increases.

Halliday & Resnick
[1988]

56.

The law that energy always moves from hot to cold which governs the direction in which natural events happen spontaneously.

Halliday & Resnick
[1988]

57.

A perpetual-motion machine of the second kind cannot be built.

Serway
[1990]

58.

The total entropy of a system and its surroundings always increases for a spontaneous process; and for a spontaneous process at a given temperature, the change in entropy of the system is greater than the heat divided by the absolute temperature.

Ebbing
[1990]

59.

LaChatelier's Principle.

Schneider & Kay
[1991]

60.

A system autonomously tending to an organized state cannot be closed.

Rosen
[1991]

61.

The entropy of the universe increases during all chemical and physical processes, but it does not require that the entropy increase take place in the reacting system itself; in open living systems, to bring about the synthesis of macromolecules from their monomer subunits, i.e. entropy decrease, free energy must be supplied to the system.

Lehniger, Nelson & Cox
[1993]

62.

As systems are moved away from equilibrium, they will utilize all avenues available to counter the applied gradients. As the applied gradients increase, so does the system’s ability to oppose further movement from equilibrium.

Schneider & Kay
[1995]

63.

A device that operates in a cycle and has no effect on the surroundings other than heat transfer from a lower-temperature body to a body at a higher temperature is impossible to construct [Clausius ‘statement’].

Black & Hart
[1996]

64.

A device that operates in a cycle and has no effect on the surroundings other than heat transfer from a single thermal energy reservoir while producing an equivalent amount of net positive work is impossible to construct.
[Kelvin-Planck ‘statement’].

Black & Hart
[1996]

65.

A ‘law of nature’ describing the behavior of physical processes as based on the observation that heat transfer alone always occurs from a high temperature to a low temperature.

Black & Hart
[1996]

66.

Everything tends towards disorder. Any process that converts energy from one form to another must lose some as heat. Perfect efficiency is impossible. The universe is a one-way street. Entropy must always increase in the universe and in any hypothetical isolated system within it.

Gleick
[1997]

67.

Nature seeks to maximize the entropy [condition: isolated system]

Nordholm
[1997]

68.

Nature seeks to minimize the free energy [condition: system of fixed volume exchanging energy with its surroundings acting as a thermal reservoir]

Nordholm
[1997]

69.

The sum of the entropy changes of a system and its exterior can never decrease.

Prigogine & Kondepudi
[1998]

70.

It is impossible to construct an engine which will work in a complete cycle, and convert all the heat it absorbs from a reservoir into mechanical work.

Prigogine & Kondepudi
[1998]

71.

Among all states available to an isolated system, there is one state, and only one, that is a stable state. This state may be reached from any state available to the system, taking into account the constraints imposed.

Perot
[1998]

72.

A principle of evolution.

Perot
[1998]

73.

Any statement affirming the existence of stable equilibrium states.

Perot
[1998]

74.

The entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process.

Chang
[1998]

75.

No irreversible engine operating between two reservoirs at constant temperatures can have a greater efficiency that a reversible engine operating between the same temperatures [Carnot’s principle].

Cuttnell & Johnson
[1998]

79.

It is impossible for any system operating in a cyclic manner to receive energy by heat transfer from a single thermal reservoir and deliver an equivalent amount of energy in the form of work to the surroundings [Kelvin-Planck statement].

Wark & Richards
[1999]

80.

It is impossible to operate any device in such a manner that the sole effect is the transfer of energy by heat transfer from a colder body to another body at a higher temperature [Clausius statement]

Wark & Richards
[1999]

81.

Any system having certain specified constraints and having an upper bound in volume can reach from any initial state a stable equilibrium state with no effect on the environment [Hatsopoulos-Keenan statement].

Wark & Richards
[1999]

82.

If a system is in stable equilibrium, no change to another stable equilibrium state can have a net work output as its sole effect external to the system.
[Hatsopoulos-Keenan corollary]

Wark & Richards
[1999]

83.

There exists an extensive, intrinsic property called entropy S.

Entropy is transported by heat transfer across the boundaries of a closed system.

The entropy transport rate associated with heat transfer at a boundary per unit time t with heat-transfer rate q/t and uniform temperature T is defined by the quantity (q/t)/T, and this quantity has the same sign convention as the heat-transfer.

Entropy can only be produced, and in the limit of an internally reversible process the rate of entropy production reduces to zero. Thus the rate of entropy production S/t for any system must satisfy the following relations: S/t > 0 for internally irreversible processes and S/t = 0 for internally reversible processes.
[Second-Law Postulate].

Wark & Richards
[1999]

84.

The law of nature which says that things wear out.

Gribbon
[2000]

85.

The spontaneous flow of energy stops when a system is at, or very near, its most likely macrostate, that is, the macrostate with the greatest multiplicity.

Schroeder
[2000]

86.

Particles and energy tend to rearrange themselves until the multiplicity is at or very near its maximum value.

Schroeder
[2000]

87.

Any large system in equilibrium will be found in the macrostate with the greatest multiplicity.

Schroeder
[2000]

88.

Multiplicity tends to increase.

Schroeder
[2000]

89.

Heat of itself cannot pass from a colder body to a hotter one; work is required.

Haynie
[2001]

90.

Cells cannot do work by heat transfer because they are isothermal systems.

Haynie
[2001]

91.

No natural process can occur unless it is accompanied by an increase in the entropy of the universe.

Haynie
[2001]

92.

No process will occur spontaneously unless it is accompanied by an increase in the entropy of the universe.

Haynie
[2001]

93.

All natural processes are irreversible and unidirectional.

Haynie
[2001]

94.

Any system not at absolute zero has some minimum amount of energy that is a necessary property of that system at that temperature; this energy, which has a magnitude TS, is isothermally unavailable.

Haynie
[2001]

95.

When energy does work, its quality, its exergy, diminishes.

Kay
[2002]

96.

It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body [Clausius-statement]

Cengel & Boles
[2002]

97.

The thermodynamic diffusion of an organic or economic system is spontaneous.

Chin
[2002]

98.

In a closed system, with no free energy input, i.e. photon input, entropy or disorder always increases; in an open system, with a continuous input of free energy, entropy always decreases.

Avery
[2003]

99.

The ratio of the heat content of a closed system to its absolute temperature always increases in any process [Clausius 'version'].

Avery
[2003]

100.

N/A

N/A
[2004]

105.

N/A

N/A
[2005]

106.

First, heat flows from hot bodies to cooler ones. Second, it is impossible entirely to convert heat into work—something is always lost in energetic transformation.

Schneider & Sagan
[2005]

107.

Nature abhors a gradient.

Schneider & Sagan
[2005]

108.

Fundamental particle interactions evolve spontaneously onto points or configurations of semi-permanent maximal stability such that the total energy of the system is minimized [tentative].

Thims
[2005]

109.

In an expanding universe fundamental particle engines evolve towards maximal efficiency [tentative].

Thims
[2005]

110.

Non-thermally-fluxed systems tend towards disintegration, or maximal disorder;
thermally-fluxed systems tend towards integration, or maximal order.

Porteus
[2005]

111.

Entropy in a closed system can never decrease.

Klyce
[2005]

112.

Things never organize themselves.

Klyce
[2005]

113.

No apparatus can operate in such a way that its only effect, in system and surroundings, is to convert heat absorbed by a system completely into work done by the system.

Smith, Van Ness & Abbott
[2005]

114.

No process is possible which consists solely in the transfer of heat from one temperature level to a higher one.

Smith, Van Ness & Abbott
[2005]

115.

It is impossible by a cyclic process to convert the heat absorbed by a system completely into work done by the system.

Smith, Van Ness & Abbott
[2005]

116.

Every process proceeds in such a direction that the total entropy change associated with it is positive, the limiting value of zero being attained only by a reversible process. No process is possible for which the total entropy decreases:
ΔS_total ≥ 0
[mathematical statement of the second law]

Smith, Van Ness & Abbott
[2005]

117.

A principle concerning prediction and evolution of systems such that if we connect a hot body to a cold one using some heat-conducting material, then the hot body will become cooler and the cold body warmer until they settle down to the same temperature.

Penrose
[2005]

118.

Entropy per baryon tends to increase relentlessly and stupendously with time.
[stipulation: positive cosmological constant]

Penrose
[2005]