1713:
other cold. Then dissipation would occur; the temperature distribution would become uniform with no work being done, and this would be irreversible because you couldn't add or remove heat or change the volume to return the system to its initial state. Thus, if the system is always uniform, then the process is reversible, meaning that you can return the system to its original state by either adding or removing heat, doing work on the system, or letting the system do work. As another example, to approximate the expansion in an internal combustion engine as reversible, we would be assuming that the temperature and pressure uniformly change throughout the volume after the spark. Obviously, this is not true and there is a
2101:
parts of the container is then opened, and the gas fills the whole container. The internal energy of the gas remains the same, while the volume increases. The original state cannot be recovered by simply compressing the gas to its original volume, since the internal energy will be increased by this compression. The original state can only be recovered by then cooling the re-compressed system, and thereby irreversibly heating the environment. The diagram to the right applies only if the first expansion is "free" (Joule expansion), i.e. there can be no atmospheric pressure outside the cylinder and no weight lifted.
2013:
1728:, which is any system of sufficient complexity, of interacting molecules is brought from one thermodynamic state to another, the configuration or arrangement of the atoms and molecules in the system will change in a way that is not easily predictable. Some "transformation energy" will be used as the molecules of the "working body" do work on each other when they change from one state to another. During this transformation, there will be some heat energy loss or
42:
1612:
1927:). The reversibility of thermodynamics must be statistical in nature; that is, it must be merely highly unlikely, but not impossible, that a system will lower in entropy. In other words, time reversibility is fulfilled if the process happens the same way if time were to flow in reverse or the order of states in the process is reversed (the last state becomes the first and vice versa).
2009:, the paradox of irreversibility can be explained in the errors associated with scaling from microstates to macrostates and the degrees of freedom used when making experimental observations. Sensitivity to initial conditions relating to the system and its environment at the microstate compounds into an exhibition of irreversible characteristics within the observable, physical realm.
1799:
1758:
1847:
1971:
However, a paradox arose when attempting to reconcile microanalysis of a system with observations of its macrostate. Many processes are mathematically reversible in their microstate when analyzed using classical
Newtonian mechanics. This paradox clearly taints microscopic explanations of macroscopic
2100:
is an example of classical thermodynamics, as it is easy to work out the resulting increase in entropy. It occurs where a volume of gas is kept in one side of a thermally isolated container (via a small partition), with the other side of the container being evacuated; the partition between the two
1712:
is irreversible because initially the system is not uniform. Initially, there is part of the system with gas in it, and part of the system with no gas. For dissipation to occur, there needs to be such a non uniformity. This is just the same as if in a system one section of the gas was hot, and the
1739:
processes that were once thought to be reversible have been found to actually be a pairing of two irreversible processes. Whereas a single enzyme was once believed to catalyze both the forward and reverse chemical changes, research has found that two separate enzymes of similar structure are
1992:
The equations of motion in abstract dynamics are perfectly reversible; any solution of these equations remains valid when the time variable t is replaced by –t. On the other hand, physical processes are irreversible: for example, the friction of solids, conduction of heat, and diffusion.
2689:
Yang, Qingling; Cong, Luping; Wang, Yujiao; Luo, Xiaoyan; Li, Hui; Wang, Huan; Zhu, Jing; Dai, Shanjun; Jin, Haixia; Yao, Guidong; Shi, Senlin; Hsueh, Aaron J.; Sun, Yingpu (20 August 2020). "Increasing ovarian NAD+ levels improve mitochondrial functions and reverse ovarian aging".
2020:: If the cylinder is a perfect insulator, the initial top-left state cannot be reached anymore after it is changed to the one on the top-right. Instead, the state on the bottom left is assumed when going back to the original pressure because energy is converted into heat.
2029:
In the physical realm, many irreversible processes are present to which the inability to achieve 100% efficiency in energy transfer can be attributed. The following is a list of spontaneous events which contribute to the irreversibility of processes.
1984:, stating that an increase of the number of possible microstates a system might be in, will increase the entropy of the system, making it less likely that the system will return to an earlier state. His formulas quantified the analysis done by
1918:
Thermodynamics defines the statistical behaviour of large numbers of entities, whose exact behavior is given by more specific laws. While the fundamental theoretical laws of physics are all time-reversible, experimentally the probability of
2733:
Tsoukalas, Dimitris; Buga, Ana; Docea, Anca; Sarandi, Evangelia; Mitrut, Radu; Renieri, Elisavet; Spandidos, Demetrios; Rogoveanu, Ion; Cercelaru, Liliana; Niculescu, Mihaela; Tsatsakis, Aristidis; Calina, Daniela (10 September 2021).
1331:
1947:
It may, moreover, happen that instead of a descending transmission of heat accompanying, in the one and the same process, the ascending transmission, another permanent change may occur which has the peculiarity of
1721:. One of the reasons that Diesel engines are able to attain higher efficiency is that the combustion is much more uniform, so less energy is lost to dissipation and the process is closer to reversible.
1685:
changes in some property of the system without expenditure of energy. A system that undergoes an irreversible process may still be capable of returning to its initial state. Because entropy is a
2153:
capacities of organisms, species or other complex systems can adapt, like minor injuries or changes in the physical environment are reversible. However, adaptation depends on import of
2149:
with the same organizational principle (e.g. identical DNA-structure) could be developed, this would not mean that the former distinct system comes back into being. Events to which the
1956:
Simply, Clausius states that it is impossible for a system to transfer heat from a cooler body to a hotter body. For example, a cup of hot coffee placed in an area of room temperature
1964:). However, that same initial cup of coffee will never absorb heat from its surroundings, causing it to grow even hotter, with the temperature of the room decreasing (to
1166:
1111:
1056:
863:
816:
731:
684:
596:
549:
2338:
Grazzini G. e Lucia U., 2008 Evolution rate of thermodynamic systems, 1st
International Workshop "Shape and Thermodynamics" – Florence 25 and 26 September 2008, pp. 1-7
1641:
767:
635:
1001:
1342:
500:
1230:
839:
792:
707:
660:
572:
525:
1993:
Nevertheless, the principle of dissipation of energy is compatible with a molecular theory in which each particle is subject to the laws of abstract dynamics.
464:
1689:, the change in entropy of the system is the same whether the process is reversible or irreversible. However, the impossibility occurs in restoring the
1320:
1353:
1939:, in the 1850s, was the first to mathematically quantify the discovery of irreversibility in nature through his introduction of the concept of
2472:
Gyenis, Balazs (2017). "Maxwell and the normal distribution: A colored story of probability, independence, and tendency towards equilibrium".
3048:
2625:
2585:
1771:
923:
1634:
1221:
457:
335:
890:
2190:
1659:
273:
1405:
1379:
900:
354:
2812:
2568:
Lebowitz, Joel L. (1995). "Microscopic reversibility and macroscopic behavior: Physical explanations and mathematical derivations".
2038:
1985:
1905:
1887:
1785:
306:
1458:
929:
328:
3043:
Lucia U., 2009, The thermodynamic
Lagrangian, in Pandalai S.G., 2009, Recent Research Developments in Physics, Vol. 8, pp. 1-5,
1943:. In his 1854 memoir "On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat," Clausius states:
1627:
2200:
1952:
without either becoming replaced by a new permanent change of a similar kind, or producing a descending transmission of heat.
1558:
90:
1981:
1453:
2423:
Lucia, U.; Maino, G. (2003). "Thermodynamical analysis of the dynamics of tumor interaction with the host immune system".
1533:
1306:
283:
2006:
1698:
918:
121:
111:
2157:
into the organism, thereby increasing irreversible processes in its environment. Ecological principles, like those of
1960:
will transfer heat to its surroundings and thereby cool down with the temperature of the room slightly increasing (to
126:
116:
1976:'s 1860 argument that molecular collisions entail an equalization of temperatures of mixed gases. From 1872 to 1875,
1865:
1817:
1448:
1410:
1374:
86:
2145:, extinction of a species or the collapse of a meteorological system can be considered as irreversible. Even if a
2069:
1968:). Therefore, the process of the coffee cooling down is irreversible unless extra energy is added to the system.
1869:
1821:
1777:
1203:
951:
397:
210:
200:
2075:
1923:
reversibility is low and the former state of system and surroundings is recovered only to certain extent (see:
1732:
due to intermolecular friction and collisions. This energy will not be recoverable if the process is reversed.
2783:
Longo, Giuseppe; Montévil, Maël (2012-01-01). Dinneen, Michael J.; Khoussainov, Bakhadyr; Nies, André (eds.).
3106:
2620:
Moran, John (2008). "Fundamentals of
Engineering Thermodynamics", p. 220. John Wiley & Sons, Inc., USA.
2180:
2162:
1655:
1615:
1443:
1240:
943:
882:
418:
407:
73:
2790:
2538:
1548:
1468:
1265:
349:
103:
78:
2862:
Lucia U., Irreversibility and entropy in
Rational Thermodynamics, Ricerche di Matematica, L1 (2001) 77-87
1857:
1813:
1924:
1690:
1674:
at the coexistence temperature (e.g. melting of ice cubes in water) is well approximated as reversible.
1483:
1060:
373:
219:
68:
2012:
2872:
Lucia, U.; Gervino, G. (2005). "Thermoeconomic analysis of an irreversible
Stirling heat pump cycle".
3074:
3008:
2969:
2934:
2891:
2647:
2491:
2432:
2395:
2360:
2305:
2235:
1725:
1563:
1488:
1478:
152:
140:
2795:
2543:
1973:
1678:
1508:
1503:
1270:
292:
258:
253:
166:
24:
2226:
Lucia, U (1995). "Mathematical consequences and
Gyarmati's principle in Rational Thermodynamics".
3026:
2907:
2881:
2818:
2715:
2671:
2591:
2507:
2481:
2321:
2251:
2175:
1597:
1260:
1208:
1121:
1066:
1011:
440:
424:
311:
263:
248:
238:
47:
41:
2960:
Lucia, U. (2007). "Irreversible entropy variation and the problem of the trend to equilibrium".
2925:
Lucia, Umberto; Maino, G. (2006). "The relativistic behaviour of the thermodynamic
Lagrangian".
1255:
845:
798:
713:
666:
578:
531:
3044:
2808:
2765:
2707:
2663:
2638:
Ledford, Heidi (2 December 2020). "Reversal of biological clock restores vision in old mice".
2621:
2581:
2205:
2118:
2109:
The difference between reversible and irreversible events has particular explanatory value in
2017:
1998:
1592:
1553:
1543:
1115:
913:
749:
741:
614:
243:
233:
175:
1681:
of a system and all of its surroundings cannot be precisely restored to its initial state by
3082:
3016:
2977:
2942:
2899:
2845:
2800:
2755:
2747:
2699:
2655:
2573:
2548:
2499:
2440:
2403:
2368:
2313:
2278:
2243:
2195:
2146:
2122:
1977:
1671:
1513:
1498:
1438:
1433:
1250:
1245:
971:
895:
363:
228:
2150:
2138:
2130:
2097:
2084:
1936:
1718:
1709:
1463:
1311:
965:
606:
429:
190:
157:
3078:
3012:
2973:
2938:
2895:
2703:
2651:
2495:
2436:
2399:
2364:
2309:
2239:
482:
2836:
Lucia, Umberto (1998). "Maximum principle and open systems including two-phase flows".
2760:
2735:
2457:
2158:
2134:
2110:
1741:
1686:
1667:
1518:
1288:
824:
777:
692:
645:
557:
510:
388:
268:
205:
195:
63:
33:
20:
2849:
2444:
2351:
Lucia, Umberto (October 2009). "Irreversibility, entropy and incomplete information".
2282:
2269:
Grazzini; Lucia, U. (1997). "Global analysis of dissipations due to irreversibility".
3100:
3030:
2911:
2719:
2675:
2255:
2058:
1682:
1587:
905:
474:
435:
147:
2822:
2595:
2511:
2325:
2296:
Lucia, U. (2008). "Probability, ergodicity, irreversibility and dynamical systems".
2789:. Lecture Notes in Computer Science. Springer Berlin Heidelberg. pp. 289–308.
2298:
Proceedings of the Royal
Society A: Mathematical, Physical and Engineering Sciences
2002:
1538:
1523:
1473:
956:
1997:
Another explanation of irreversible systems was presented by French mathematician
2903:
2804:
2001:. In 1890, he published his first explanation of nonlinear dynamics, also called
3086:
2981:
2946:
2503:
2407:
2372:
2126:
2037:(this claim is disputed, as aging has been demonstrated to be reversed in mice.
1729:
1714:
1705:
1493:
301:
2659:
2386:
Lucia, U (2008). "Statistical approach of the irreversible entropy variation".
3021:
2996:
2553:
2526:
2154:
2114:
2042:
1701:
can be used to determine whether a hypothetical process is reversible or not.
1582:
1528:
2577:
2137:. In the context of complex systems, events which lead to the end of certain
2608:
180:
2997:"Hydrodynamics cavitation: from theory towards a new experimental approach"
2769:
2751:
2736:"Reversal of brain aging by targeting telomerase: A nutraceutical approach"
2711:
2667:
2317:
1693:
to its own initial conditions. An irreversible process increases the total
3065:
Lucia, U. (2010). "Maximum entropy generation and κκ-exponential model".
2064:
1296:
1213:
1005:
413:
185:
2886:
2247:
1940:
1736:
1694:
402:
1980:
reinforced the statistical explanation of this paradox in the form of
2185:
2034:
3059:
Lucia U., 2010, Maximum entropy generation and κ−exponential model,
2784:
2486:
2129:, which enables their continued existence. More primitive forms of
2142:
2048:
2011:
1724:
The phenomenon of irreversibility results from the fact that if a
2420:
Lucia U., "Irreversible
Entropy in Biological Systems", EPISTEME
2053:
378:
2165:
can be defined with reference to the concept of reversibility.
1840:
1792:
1751:
1670:. All complex natural processes are irreversible, although a
2572:. Lecture Notes in Physics. Vol. 445. pp. 1–20.
2092:
Spontaneous mixing of matter of varying composition/states
2133:
systems have been described by the physicist and chemist
1740:
typically needed to perform what results in a pair of
3067:
Physica A: Statistical Mechanics and Its Applications
2962:
Physica A: Statistical Mechanics and Its Applications
2425:
Physica A: Statistical Mechanics and Its Applications
2388:
Physica A: Statistical Mechanics and Its Applications
2353:
Physica A: Statistical Mechanics and Its Applications
1124:
1069:
1014:
974:
848:
827:
801:
780:
752:
716:
695:
669:
648:
617:
581:
560:
534:
513:
485:
1704:
Intuitively, a process is reversible if there is no
2474:
Studies in History and Philosophy of Modern Physics
1808:may lack focus or may be about more than one topic
1160:
1105:
1050:
995:
857:
833:
810:
786:
761:
725:
701:
678:
654:
629:
590:
566:
543:
519:
494:
2570:25 Years of Non-Equilibrium Statistical Mechanics
2080:Magnetization or polarization with a hysteresis
2045:have also been demonstrated to reverse ageing.)
1990:
1945:
2611:.Page dated 2002-2-19. Retrieved on 2010-4-01.
1812:Please help improve this article, possibly by
2525:Bishop, R. C.; Bohm, A.; Gadella, M. (2004).
1635:
8:
1868:. There might be a discussion about this on
19:For the concept in evolutionary theory, see
2740:International Journal of Molecular Medicine
2346:
2344:
1786:Learn how and when to remove these messages
1642:
1628:
1191:
343:
162:
40:
29:
3020:
2885:
2794:
2759:
2552:
2542:
2485:
1906:Learn how and when to remove this message
1888:Learn how and when to remove this message
1748:Absolute versus statistical reversibility
1123:
1068:
1013:
973:
847:
826:
800:
779:
751:
715:
694:
668:
647:
616:
580:
559:
533:
512:
484:
2125:, living organisms are characterized by
1697:of the system and its surroundings. The
2531:Discrete Dynamics in Nature and Society
2218:
2061:through a finite temperature difference
1388:
1365:
1319:
1279:
1229:
1194:
387:
362:
291:
218:
165:
32:
2527:"Irreversibility in quantum mechanics"
1972:tendency towards equilibrium, such as
7:
1816:the article and/or by introducing a
1666:. This concept arises frequently in
3001:Central European Journal of Physics
2704:10.1016/j.freeradbiomed.2020.05.003
2191:Reversible process (thermodynamics)
2074:Flow of electric current through a
1677:In thermodynamics, a change in the
2025:Examples of irreversible processes
849:
802:
717:
670:
582:
535:
355:Intensive and extensive properties
14:
2692:Free Radical Biology and Medicine
1986:William Thomson, 1st Baron Kelvin
1767:This section has multiple issues.
1845:
1797:
1756:
1611:
1610:
930:Table of thermodynamic equations
2995:Lucia, U.; Gervino, G. (2009).
2874:The European Physical Journal B
2786:Computation, Physics and Beyond
2609:"The 2nd Law of Thermodynamics"
2117:). According to the biologists
2005:. Applying chaos theory to the
1820:, or discuss this issue on the
1775:or discuss these issues on the
1406:Maxwell's thermodynamic surface
2201:Non-equilibrium thermodynamics
2113:(such as living organisms, or
2089:Spontaneous chemical reactions
1140:
1128:
1085:
1073:
1030:
1018:
990:
978:
1:
2850:10.1016/s0035-3159(98)80007-x
2445:10.1016/S0378-4371(02)00980-9
2283:10.1016/s0035-3159(97)89987-4
1307:Mechanical equivalent of heat
16:Process that cannot be undone
2805:10.1007/978-3-642-27654-5_22
2007:second law of thermodynamics
1699:second law of thermodynamics
919:Onsager reciprocal relations
3087:10.1016/j.physa.2010.06.047
2982:10.1016/j.physa.2006.10.059
2838:Revue Gènèrale de Thermique
2504:10.1016/j.shpsb.2017.01.001
2408:10.1016/j.physa.2008.02.002
2373:10.1016/j.physa.2009.06.027
2271:Revue Gènèrale de Thermique
1982:Boltzmann's entropy formula
1411:Entropy as energy dispersal
1222:"Perpetual motion" machines
1161:{\displaystyle G(T,p)=H-TS}
1106:{\displaystyle A(T,V)=U-TS}
1051:{\displaystyle H(S,p)=U+pV}
3123:
2904:10.1140/epjb/e2006-00060-x
2660:10.1038/d41586-020-03403-0
858:{\displaystyle \partial T}
811:{\displaystyle \partial V}
726:{\displaystyle \partial p}
679:{\displaystyle \partial V}
591:{\displaystyle \partial T}
544:{\displaystyle \partial S}
18:
3022:10.2478/s11534-009-0092-y
2947:10.1393/ncb/i2006-10035-8
2554:10.1155/S1026022604401046
1332:An Inquiry Concerning the
2578:10.1007/3-540-59158-3_31
1744:irreversible processes.
1345:Heterogeneous Substances
762:{\displaystyle \alpha =}
630:{\displaystyle \beta =-}
2181:Entropy (arrow of time)
2163:precautionary principle
1988:, who had argued that:
2752:10.3892/ijmm.2021.5032
2318:10.1098/rspa.2007.0304
2021:
1995:
1954:
1162:
1107:
1052:
997:
996:{\displaystyle U(S,V)}
859:
835:
812:
788:
763:
727:
703:
680:
656:
631:
592:
568:
545:
521:
496:
475:Specific heat capacity
79:Quantum thermodynamics
23:. For other uses, see
2015:
1935:The German physicist
1925:uncertainty principle
1343:On the Equilibrium of
1163:
1108:
1061:Helmholtz free energy
1053:
998:
860:
836:
813:
789:
764:
728:
704:
681:
657:
632:
593:
569:
546:
522:
497:
3063:389, pp. 4558-4563
1950:not being reversible
1858:confusing or unclear
1726:thermodynamic system
1356:Motive Power of Fire
1122:
1067:
1012:
972:
924:Bridgman's equations
901:Fundamental relation
846:
825:
799:
778:
750:
714:
693:
667:
646:
615:
579:
558:
532:
511:
483:
3079:2010PhyA..389.4558L
3013:2009CEJPh...7..638L
2974:2007PhyA..376..289L
2939:2006NCimB.121..213L
2896:2006EPJB...50..367L
2652:2020Natur.588..209L
2496:2017SHPMP..57...53G
2437:2002PhyA..313..569L
2400:2008PhyA..387.3454L
2365:2009PhyA..388.4025L
2310:2008RSPSA.464.1089L
2304:(2093): 1089–1104.
2240:1995NCimB.110.1227L
2085:expansion of fluids
2070:Plastic deformation
1974:James Clerk Maxwell
1866:clarify the section
1818:disambiguation page
1717:and sometimes even
1679:thermodynamic state
1334:Source ... Friction
1266:Loschmidt's paradox
458:Material properties
336:Conjugate variables
25:Reversible dynamics
2927:Il Nuovo Cimento B
2248:10.1007/bf02724612
2176:Entropy production
2022:
1598:Order and disorder
1354:Reflections on the
1261:Heat death paradox
1158:
1103:
1048:
993:
855:
831:
808:
784:
759:
723:
699:
676:
652:
627:
588:
564:
541:
517:
495:{\displaystyle c=}
492:
465:Property databases
441:Reduced properties
425:Chemical potential
389:Functions of state
312:Thermal efficiency
48:Carnot heat engine
3073:(21): 4558–4563.
3049:978-81-7895-346-5
2626:978-0-471-78735-8
2587:978-3-540-59158-0
2394:(14): 3454–3460.
2359:(19): 4025–4033.
2234:(10): 1227–1235.
2206:Symmetry breaking
2119:Humberto Maturana
2018:adiabatic process
1916:
1915:
1908:
1898:
1897:
1890:
1839:
1838:
1790:
1742:thermodynamically
1652:
1651:
1593:Self-organization
1418:
1417:
1116:Gibbs free energy
914:Maxwell relations
872:
871:
868:
867:
834:{\displaystyle V}
787:{\displaystyle 1}
742:Thermal expansion
736:
735:
702:{\displaystyle V}
655:{\displaystyle 1}
601:
600:
567:{\displaystyle N}
520:{\displaystyle T}
448:
447:
364:Process functions
350:Property diagrams
329:System properties
319:
318:
284:Endoreversibility
176:Equation of state
3114:
3091:
3090:
3057:
3051:
3041:
3035:
3034:
3024:
2992:
2986:
2985:
2957:
2951:
2950:
2922:
2916:
2915:
2889:
2880:(1–2): 367–369.
2869:
2863:
2860:
2854:
2853:
2833:
2827:
2826:
2798:
2780:
2774:
2773:
2763:
2730:
2724:
2723:
2686:
2680:
2679:
2635:
2629:
2618:
2612:
2606:
2600:
2599:
2565:
2559:
2558:
2556:
2546:
2522:
2516:
2515:
2489:
2469:
2463:
2458:David Albert on
2455:
2449:
2448:
2431:(3–4): 569–577.
2418:
2412:
2411:
2383:
2377:
2376:
2348:
2339:
2336:
2330:
2329:
2293:
2287:
2286:
2266:
2260:
2259:
2228:Il Nuovo Cimento
2223:
2196:One way function
2141:processes, like
2123:Francisco Varela
1978:Ludwig Boltzmann
1967:
1963:
1959:
1911:
1904:
1893:
1886:
1882:
1879:
1873:
1849:
1848:
1841:
1834:
1831:
1825:
1801:
1800:
1793:
1782:
1760:
1759:
1752:
1672:phase transition
1644:
1637:
1630:
1614:
1613:
1321:Key publications
1302:
1301:("living force")
1251:Brownian ratchet
1246:Entropy and life
1241:Entropy and time
1192:
1167:
1165:
1164:
1159:
1112:
1110:
1109:
1104:
1057:
1055:
1054:
1049:
1002:
1000:
999:
994:
896:Clausius theorem
891:Carnot's theorem
864:
862:
861:
856:
840:
838:
837:
832:
817:
815:
814:
809:
793:
791:
790:
785:
772:
771:
768:
766:
765:
760:
732:
730:
729:
724:
708:
706:
705:
700:
685:
683:
682:
677:
661:
659:
658:
653:
640:
639:
636:
634:
633:
628:
597:
595:
594:
589:
573:
571:
570:
565:
550:
548:
547:
542:
526:
524:
523:
518:
505:
504:
501:
499:
498:
493:
471:
470:
344:
163:
44:
30:
3122:
3121:
3117:
3116:
3115:
3113:
3112:
3111:
3097:
3096:
3095:
3094:
3064:
3058:
3054:
3042:
3038:
2994:
2993:
2989:
2959:
2958:
2954:
2924:
2923:
2919:
2887:physics/0512182
2871:
2870:
2866:
2861:
2857:
2835:
2834:
2830:
2815:
2796:10.1.1.640.1835
2782:
2781:
2777:
2732:
2731:
2727:
2688:
2687:
2683:
2637:
2636:
2632:
2619:
2615:
2607:
2603:
2588:
2567:
2566:
2562:
2544:10.1.1.576.7850
2524:
2523:
2519:
2471:
2470:
2466:
2460:Time and Chance
2456:
2452:
2422:
2421:
2419:
2415:
2385:
2384:
2380:
2350:
2349:
2342:
2337:
2333:
2295:
2294:
2290:
2268:
2267:
2263:
2225:
2224:
2220:
2215:
2210:
2171:
2151:self-organizing
2139:self-organising
2131:self-organizing
2111:complex systems
2107:
2105:Complex systems
2098:Joule expansion
2027:
1965:
1961:
1957:
1937:Rudolf Clausius
1933:
1912:
1901:
1900:
1899:
1894:
1883:
1877:
1874:
1863:
1850:
1846:
1835:
1829:
1826:
1811:
1802:
1798:
1761:
1757:
1750:
1719:engine knocking
1710:Joule expansion
1708:. For example,
1648:
1603:
1602:
1578:
1570:
1569:
1568:
1428:
1420:
1419:
1398:
1384:
1359:
1355:
1348:
1344:
1337:
1333:
1300:
1293:
1275:
1256:Maxwell's demon
1218:
1189:
1188:
1172:
1171:
1170:
1120:
1119:
1118:
1065:
1064:
1063:
1010:
1009:
1008:
970:
969:
968:
966:Internal energy
961:
946:
936:
935:
910:
885:
875:
874:
873:
844:
843:
823:
822:
797:
796:
776:
775:
748:
747:
712:
711:
691:
690:
665:
664:
644:
643:
613:
612:
607:Compressibility
577:
576:
556:
555:
530:
529:
509:
508:
481:
480:
460:
450:
449:
430:Particle number
383:
342:
331:
321:
320:
279:Irreversibility
191:State of matter
158:Isolated system
143:
133:
132:
131:
106:
96:
95:
91:Non-equilibrium
83:
58:
50:
28:
17:
12:
11:
5:
3120:
3118:
3110:
3109:
3107:Thermodynamics
3099:
3098:
3093:
3092:
3052:
3036:
3007:(3): 638–644.
2987:
2952:
2933:(2): 213–216.
2917:
2864:
2855:
2844:(9): 813–817.
2828:
2813:
2775:
2725:
2681:
2630:
2613:
2601:
2586:
2560:
2517:
2464:
2450:
2413:
2378:
2340:
2331:
2288:
2277:(8): 605–609.
2261:
2217:
2216:
2214:
2211:
2209:
2208:
2203:
2198:
2193:
2188:
2183:
2178:
2172:
2170:
2167:
2159:sustainability
2135:Ilya Prigogine
2106:
2103:
2094:
2093:
2090:
2087:
2081:
2078:
2072:
2067:
2062:
2056:
2051:
2046:
2026:
2023:
1999:Henri Poincaré
1932:
1929:
1914:
1913:
1896:
1895:
1853:
1851:
1844:
1837:
1836:
1805:
1803:
1796:
1791:
1765:
1764:
1762:
1755:
1749:
1746:
1687:state function
1668:thermodynamics
1654:In science, a
1650:
1649:
1647:
1646:
1639:
1632:
1624:
1621:
1620:
1619:
1618:
1605:
1604:
1601:
1600:
1595:
1590:
1585:
1579:
1576:
1575:
1572:
1571:
1567:
1566:
1561:
1556:
1551:
1546:
1541:
1536:
1531:
1526:
1521:
1516:
1511:
1506:
1501:
1496:
1491:
1486:
1481:
1476:
1471:
1466:
1461:
1456:
1451:
1446:
1441:
1436:
1430:
1429:
1426:
1425:
1422:
1421:
1416:
1415:
1414:
1413:
1408:
1400:
1399:
1397:
1396:
1393:
1389:
1386:
1385:
1383:
1382:
1377:
1375:Thermodynamics
1371:
1368:
1367:
1363:
1362:
1361:
1360:
1351:
1349:
1340:
1338:
1329:
1324:
1323:
1317:
1316:
1315:
1314:
1309:
1304:
1292:
1291:
1289:Caloric theory
1285:
1282:
1281:
1277:
1276:
1274:
1273:
1268:
1263:
1258:
1253:
1248:
1243:
1237:
1234:
1233:
1227:
1226:
1225:
1224:
1217:
1216:
1211:
1206:
1200:
1197:
1196:
1190:
1187:
1186:
1183:
1179:
1178:
1177:
1174:
1173:
1169:
1168:
1157:
1154:
1151:
1148:
1145:
1142:
1139:
1136:
1133:
1130:
1127:
1113:
1102:
1099:
1096:
1093:
1090:
1087:
1084:
1081:
1078:
1075:
1072:
1058:
1047:
1044:
1041:
1038:
1035:
1032:
1029:
1026:
1023:
1020:
1017:
1003:
992:
989:
986:
983:
980:
977:
962:
960:
959:
954:
948:
947:
942:
941:
938:
937:
934:
933:
926:
921:
916:
909:
908:
903:
898:
893:
887:
886:
881:
880:
877:
876:
870:
869:
866:
865:
854:
851:
841:
830:
819:
818:
807:
804:
794:
783:
769:
758:
755:
745:
738:
737:
734:
733:
722:
719:
709:
698:
687:
686:
675:
672:
662:
651:
637:
626:
623:
620:
610:
603:
602:
599:
598:
587:
584:
574:
563:
552:
551:
540:
537:
527:
516:
502:
491:
488:
478:
469:
468:
467:
461:
456:
455:
452:
451:
446:
445:
444:
443:
438:
433:
422:
411:
392:
391:
385:
384:
382:
381:
376:
370:
367:
366:
360:
359:
358:
357:
352:
333:
332:
327:
326:
323:
322:
317:
316:
315:
314:
309:
304:
296:
295:
289:
288:
287:
286:
281:
276:
271:
269:Free expansion
266:
261:
256:
251:
246:
241:
236:
231:
223:
222:
216:
215:
214:
213:
208:
206:Control volume
203:
198:
196:Phase (matter)
193:
188:
183:
178:
170:
169:
161:
160:
155:
150:
144:
139:
138:
135:
134:
130:
129:
124:
119:
114:
108:
107:
102:
101:
98:
97:
94:
93:
82:
81:
76:
71:
66:
60:
59:
56:
55:
52:
51:
46:The classical
45:
37:
36:
34:Thermodynamics
15:
13:
10:
9:
6:
4:
3:
2:
3119:
3108:
3105:
3104:
3102:
3088:
3084:
3080:
3076:
3072:
3068:
3062:
3056:
3053:
3050:
3046:
3040:
3037:
3032:
3028:
3023:
3018:
3014:
3010:
3006:
3002:
2998:
2991:
2988:
2983:
2979:
2975:
2971:
2967:
2963:
2956:
2953:
2948:
2944:
2940:
2936:
2932:
2928:
2921:
2918:
2913:
2909:
2905:
2901:
2897:
2893:
2888:
2883:
2879:
2875:
2868:
2865:
2859:
2856:
2851:
2847:
2843:
2839:
2832:
2829:
2824:
2820:
2816:
2814:9783642276538
2810:
2806:
2802:
2797:
2792:
2788:
2787:
2779:
2776:
2771:
2767:
2762:
2757:
2753:
2749:
2745:
2741:
2737:
2729:
2726:
2721:
2717:
2713:
2709:
2705:
2701:
2697:
2693:
2685:
2682:
2677:
2673:
2669:
2665:
2661:
2657:
2653:
2649:
2646:(7837): 209.
2645:
2641:
2634:
2631:
2627:
2623:
2617:
2614:
2610:
2605:
2602:
2597:
2593:
2589:
2583:
2579:
2575:
2571:
2564:
2561:
2555:
2550:
2545:
2540:
2536:
2532:
2528:
2521:
2518:
2513:
2509:
2505:
2501:
2497:
2493:
2488:
2483:
2479:
2475:
2468:
2465:
2462:
2461:
2454:
2451:
2446:
2442:
2438:
2434:
2430:
2426:
2417:
2414:
2409:
2405:
2401:
2397:
2393:
2389:
2382:
2379:
2374:
2370:
2366:
2362:
2358:
2354:
2347:
2345:
2341:
2335:
2332:
2327:
2323:
2319:
2315:
2311:
2307:
2303:
2299:
2292:
2289:
2284:
2280:
2276:
2272:
2265:
2262:
2257:
2253:
2249:
2245:
2241:
2237:
2233:
2229:
2222:
2219:
2212:
2207:
2204:
2202:
2199:
2197:
2194:
2192:
2189:
2187:
2184:
2182:
2179:
2177:
2174:
2173:
2168:
2166:
2164:
2160:
2156:
2152:
2148:
2144:
2140:
2136:
2132:
2128:
2124:
2120:
2116:
2112:
2104:
2102:
2099:
2091:
2088:
2086:
2083:Unrestrained
2082:
2079:
2077:
2073:
2071:
2068:
2066:
2063:
2060:
2059:Heat transfer
2057:
2055:
2052:
2050:
2047:
2044:
2040:
2036:
2033:
2032:
2031:
2024:
2019:
2016:Irreversible
2014:
2010:
2008:
2004:
2000:
1994:
1989:
1987:
1983:
1979:
1975:
1969:
1953:
1951:
1944:
1942:
1938:
1930:
1928:
1926:
1922:
1910:
1907:
1892:
1889:
1881:
1871:
1870:the talk page
1867:
1861:
1859:
1854:This section
1852:
1843:
1842:
1833:
1823:
1819:
1815:
1809:
1806:This article
1804:
1795:
1794:
1789:
1787:
1780:
1779:
1774:
1773:
1768:
1763:
1754:
1753:
1747:
1745:
1743:
1738:
1733:
1731:
1727:
1722:
1720:
1716:
1711:
1707:
1702:
1700:
1696:
1692:
1688:
1684:
1683:infinitesimal
1680:
1675:
1673:
1669:
1665:
1661:
1657:
1645:
1640:
1638:
1633:
1631:
1626:
1625:
1623:
1622:
1617:
1609:
1608:
1607:
1606:
1599:
1596:
1594:
1591:
1589:
1588:Self-assembly
1586:
1584:
1581:
1580:
1574:
1573:
1565:
1562:
1560:
1559:van der Waals
1557:
1555:
1552:
1550:
1547:
1545:
1542:
1540:
1537:
1535:
1532:
1530:
1527:
1525:
1522:
1520:
1517:
1515:
1512:
1510:
1507:
1505:
1502:
1500:
1497:
1495:
1492:
1490:
1487:
1485:
1484:von Helmholtz
1482:
1480:
1477:
1475:
1472:
1470:
1467:
1465:
1462:
1460:
1457:
1455:
1452:
1450:
1447:
1445:
1442:
1440:
1437:
1435:
1432:
1431:
1424:
1423:
1412:
1409:
1407:
1404:
1403:
1402:
1401:
1394:
1391:
1390:
1387:
1381:
1378:
1376:
1373:
1372:
1370:
1369:
1364:
1358:
1357:
1350:
1347:
1346:
1339:
1336:
1335:
1328:
1327:
1326:
1325:
1322:
1318:
1313:
1310:
1308:
1305:
1303:
1299:
1295:
1294:
1290:
1287:
1286:
1284:
1283:
1278:
1272:
1269:
1267:
1264:
1262:
1259:
1257:
1254:
1252:
1249:
1247:
1244:
1242:
1239:
1238:
1236:
1235:
1232:
1228:
1223:
1220:
1219:
1215:
1212:
1210:
1207:
1205:
1202:
1201:
1199:
1198:
1193:
1184:
1181:
1180:
1176:
1175:
1155:
1152:
1149:
1146:
1143:
1137:
1134:
1131:
1125:
1117:
1114:
1100:
1097:
1094:
1091:
1088:
1082:
1079:
1076:
1070:
1062:
1059:
1045:
1042:
1039:
1036:
1033:
1027:
1024:
1021:
1015:
1007:
1004:
987:
984:
981:
975:
967:
964:
963:
958:
955:
953:
950:
949:
945:
940:
939:
932:
931:
927:
925:
922:
920:
917:
915:
912:
911:
907:
906:Ideal gas law
904:
902:
899:
897:
894:
892:
889:
888:
884:
879:
878:
852:
842:
828:
821:
820:
805:
795:
781:
774:
773:
770:
756:
753:
746:
743:
740:
739:
720:
710:
696:
689:
688:
673:
663:
649:
642:
641:
638:
624:
621:
618:
611:
608:
605:
604:
585:
575:
561:
554:
553:
538:
528:
514:
507:
506:
503:
489:
486:
479:
476:
473:
472:
466:
463:
462:
459:
454:
453:
442:
439:
437:
436:Vapor quality
434:
432:
431:
426:
423:
421:
420:
415:
412:
409:
405:
404:
399:
396:
395:
394:
393:
390:
386:
380:
377:
375:
372:
371:
369:
368:
365:
361:
356:
353:
351:
348:
347:
346:
345:
341:
337:
330:
325:
324:
313:
310:
308:
305:
303:
300:
299:
298:
297:
294:
290:
285:
282:
280:
277:
275:
274:Reversibility
272:
270:
267:
265:
262:
260:
257:
255:
252:
250:
247:
245:
242:
240:
237:
235:
232:
230:
227:
226:
225:
224:
221:
217:
212:
209:
207:
204:
202:
199:
197:
194:
192:
189:
187:
184:
182:
179:
177:
174:
173:
172:
171:
168:
164:
159:
156:
154:
151:
149:
148:Closed system
146:
145:
142:
137:
136:
128:
125:
123:
120:
118:
115:
113:
110:
109:
105:
100:
99:
92:
88:
85:
84:
80:
77:
75:
72:
70:
67:
65:
62:
61:
54:
53:
49:
43:
39:
38:
35:
31:
26:
22:
3070:
3066:
3060:
3055:
3039:
3004:
3000:
2990:
2965:
2961:
2955:
2930:
2926:
2920:
2877:
2873:
2867:
2858:
2841:
2837:
2831:
2785:
2778:
2743:
2739:
2728:
2695:
2691:
2684:
2643:
2639:
2633:
2616:
2604:
2569:
2563:
2537:(1): 75–83.
2534:
2530:
2520:
2477:
2473:
2467:
2459:
2453:
2428:
2424:
2416:
2391:
2387:
2381:
2356:
2352:
2334:
2301:
2297:
2291:
2274:
2270:
2264:
2231:
2227:
2221:
2108:
2095:
2028:
2003:chaos theory
1996:
1991:
1970:
1955:
1949:
1946:
1934:
1920:
1917:
1902:
1884:
1875:
1864:Please help
1855:
1827:
1807:
1783:
1776:
1770:
1769:Please help
1766:
1734:
1723:
1703:
1676:
1664:irreversible
1663:
1658:that is not
1653:
1449:Carathéodory
1380:Heat engines
1352:
1341:
1330:
1312:Motive power
1297:
957:Free entropy
928:
428:
427: /
417:
416: /
408:introduction
401:
400: /
339:
302:Heat engines
278:
89: /
2968:: 289–292.
2127:autopoiesis
1730:dissipation
1715:flame front
1706:dissipation
1691:environment
1271:Synergetics
952:Free energy
398:Temperature
259:Quasistatic
254:Isenthalpic
211:Instruments
201:Equilibrium
153:Open system
87:Equilibrium
69:Statistical
21:Dollo's law
2746:(5): 199.
2487:1702.01411
2213:References
2155:negentropy
2115:ecosystems
2076:resistance
2043:telomerase
1878:April 2014
1860:to readers
1830:April 2014
1772:improve it
1737:biological
1662:is called
1660:reversible
1583:Nucleation
1427:Scientists
1231:Philosophy
944:Potentials
307:Heat pumps
264:Polytropic
249:Isentropic
239:Isothermal
3061:Physica A
3031:120720503
2912:119372773
2791:CiteSeerX
2720:219312914
2676:227259860
2539:CiteSeerX
2480:: 53–65.
2256:119568672
1822:talk page
1814:splitting
1778:talk page
1564:Waterston
1514:von Mayer
1469:de Donder
1459:Clapeyron
1439:Boltzmann
1434:Bernoulli
1395:Education
1366:Timelines
1150:−
1095:−
883:Equations
850:∂
803:∂
754:α
718:∂
671:∂
625:−
619:β
583:∂
536:∂
244:Adiabatic
234:Isochoric
220:Processes
181:Ideal gas
64:Classical
3101:Category
2823:16929949
2770:34515324
2712:32492457
2698:: 1–10.
2668:33268879
2596:16589172
2512:38272381
2326:34898343
2169:See also
2161:and the
2065:Friction
1966:~71.7 °F
1962:~72.3 °F
1958:(~72 °F)
1616:Category
1554:Thompson
1464:Clausius
1444:Bridgman
1298:Vis viva
1280:Theories
1214:Gas laws
1006:Enthalpy
414:Pressure
229:Isobaric
186:Real gas
74:Chemical
57:Branches
3075:Bibcode
3009:Bibcode
2970:Bibcode
2935:Bibcode
2892:Bibcode
2761:8448543
2648:Bibcode
2492:Bibcode
2433:Bibcode
2396:Bibcode
2361:Bibcode
2306:Bibcode
2236:Bibcode
1941:entropy
1931:History
1856:may be
1695:entropy
1656:process
1539:Smeaton
1534:Rankine
1524:Onsager
1509:Maxwell
1504:Massieu
1209:Entropy
1204:General
1195:History
1185:Culture
1182:History
406: (
403:Entropy
340:italics
141:Systems
3047:
3029:
2910:
2821:
2811:
2793:
2768:
2758:
2718:
2710:
2674:
2666:
2640:Nature
2624:
2594:
2584:
2541:
2510:
2324:
2254:
2186:Exergy
2035:Ageing
1529:Planck
1519:Nernst
1494:Kelvin
1454:Carnot
744:
609:
477:
419:Volume
334:Note:
293:Cycles
122:Second
112:Zeroth
3027:S2CID
2908:S2CID
2882:arXiv
2819:S2CID
2716:S2CID
2672:S2CID
2592:S2CID
2508:S2CID
2482:arXiv
2322:S2CID
2252:S2CID
2147:clone
2143:death
2049:Death
1735:Many
1577:Other
1544:Stahl
1499:Lewis
1489:Joule
1479:Gibbs
1474:Duhem
167:State
127:Third
117:First
3045:ISBN
2809:ISBN
2766:PMID
2708:PMID
2664:PMID
2622:ISBN
2582:ISBN
2535:2004
2232:B110
2121:and
2054:Time
2041:and
2039:NAD+
1921:real
1549:Tait
379:Heat
374:Work
104:Laws
3083:doi
3071:389
3017:doi
2978:doi
2966:376
2943:doi
2931:121
2900:doi
2846:doi
2801:doi
2756:PMC
2748:doi
2700:doi
2696:156
2656:doi
2644:588
2574:doi
2549:doi
2500:doi
2441:doi
2429:313
2404:doi
2392:387
2369:doi
2357:388
2314:doi
2302:464
2279:doi
2244:doi
1392:Art
338:in
3103::
3081:.
3069:.
3025:.
3015:.
3003:.
2999:.
2976:.
2964:.
2941:.
2929:.
2906:.
2898:.
2890:.
2878:50
2876:.
2842:37
2840:.
2817:.
2807:.
2799:.
2764:.
2754:.
2744:48
2742:.
2738:.
2714:.
2706:.
2694:.
2670:.
2662:.
2654:.
2642:.
2590:.
2580:.
2547:.
2533:.
2529:.
2506:.
2498:.
2490:.
2478:57
2476:.
2439:.
2427:.
2402:.
2390:.
2367:.
2355:.
2343:^
2320:.
2312:.
2300:.
2275:36
2273:.
2250:.
2242:.
2230:.
2096:A
1781:.
3089:.
3085::
3077::
3033:.
3019::
3011::
3005:7
2984:.
2980::
2972::
2949:.
2945::
2937::
2914:.
2902::
2894::
2884::
2852:.
2848::
2825:.
2803::
2772:.
2750::
2722:.
2702::
2678:.
2658::
2650::
2628:.
2598:.
2576::
2557:.
2551::
2514:.
2502::
2494::
2484::
2447:.
2443::
2435::
2410:.
2406::
2398::
2375:.
2371::
2363::
2328:.
2316::
2308::
2285:.
2281::
2258:.
2246::
2238::
1909:)
1903:(
1891:)
1885:(
1880:)
1876:(
1872:.
1862:.
1832:)
1828:(
1824:.
1810:.
1788:)
1784:(
1643:e
1636:t
1629:v
1156:S
1153:T
1147:H
1144:=
1141:)
1138:p
1135:,
1132:T
1129:(
1126:G
1101:S
1098:T
1092:U
1089:=
1086:)
1083:V
1080:,
1077:T
1074:(
1071:A
1046:V
1043:p
1040:+
1037:U
1034:=
1031:)
1028:p
1025:,
1022:S
1019:(
1016:H
991:)
988:V
985:,
982:S
979:(
976:U
853:T
829:V
806:V
782:1
757:=
721:p
697:V
674:V
650:1
622:=
586:T
562:N
539:S
515:T
490:=
487:c
410:)
27:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
