Knowledge (XXG)

Molecular chaos

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417: 45:) is the assumption that the velocities of colliding particles are uncorrelated, and independent of position. This means the probability that a pair of particles with given velocities will collide can be calculated by considering each particle separately and ignoring any correlation between the probability for finding one particle with velocity 102:
are no longer truly uncorrelated. By asserting that it was acceptable to ignore these correlations in the population at times after the initial time, Boltzmann had introduced an element of time asymmetry through the formalism of his calculation.
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of 1872, which attempted to use kinetic theory to show that the entropy of a gas prepared in a state of less than complete disorder must inevitably increase, as the gas molecules are allowed to collide. This drew the objection from
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is usually understood as a physically grounded hypothesis, it was recently highlighted that it could also be interpreted as a heuristic hypothesis. This interpretation allows using the
477: 458: 81:, by reducing the 2-particle distribution function showing up in the collision term to a product of 1-particle distributions. This in turn leads to Boltzmann's 248:"Illustrations of the dynamical theory of gases. Part II. On the process of diffusion of two or more kinds of moving particles among one another," 451: 416: 269:
Gyenis, Balazs (2017). "Maxwell and the normal distribution: A colored story of probability, independence, and tendency towards equilibrium".
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Brown, Harvey R.; Myrvold, Wayne (2008-09-08). "Boltzmann's H-theorem, its limitations, and the birth of (fully) statistical mechanics".
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introduced this approximation in 1867 although its origins can be traced back to his first work on the kinetic theory in 1860.
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The assumption of molecular chaos is the key ingredient that allows proceeding from the
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from time-symmetric dynamics and a time-symmetric formalism: something must be wrong (
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Boltzmann, L. (2003). "Further Studies on the Thermal Equilibrium of Gas Molecules".
308: 216: 98:). The resolution (1895) of this paradox is that the velocities of two particles 300: 346: 87: 82: 208: 24: 396: 371: 333:. History of Modern Physical Sciences. Vol. 1. pp. 262–349. 325:." Sitzungsberichte Akademie der Wissenschaften 66 (1872): 275-370. 283: 150:
The Conceptual Foundations of the Statistical Approach in Mechanics
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Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen
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Maxwell, J. C. (1867). "On the Dynamical Theory of Gases".
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Philosophical Transactions of the Royal Society of London
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Chliamovitch, G.; Malaspinas, O.; Chopard, B. (2017).
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Studies in History and Philosophy of Modern Physics
478:Philosophy of thermal and statistical physics 452: 51:and probability for finding another velocity 8: 147:Ehrenfest, Paul; Ehrenfest, Tatiana (2002). 90:that it should not be possible to deduce an 372:"Kinetic theory beyond the Stosszahlansatz" 459: 445: 395: 282: 179: 16:Assumption in the kinetic theory of gases 118:to higher-order distribution functions. 139: 7: 413: 411: 431:. You can help Knowledge (XXG) by 14: 415: 29:the molecular chaos hypothesis 1: 112:principle of maximum entropy 488:Statistical mechanics stubs 331:The Kinetic Theory of Gases 301:10.1016/j.shpsb.2017.01.001 114:in order to generalize the 504: 410: 347:10.1142/9781848161337_0015 153:. Courier Corporation. 21:kinetic theory of gases 251:Philosophical Magazine 237:Philosophical Magazine 209:10.1098/rstl.1867.0004 483:Statistical mechanics 425:statistical mechanics 327:English translation: 246:Maxwell, J.C. (1860) 232:Maxwell, J.C. (1860) 92:irreversible process 79:Boltzmann's equation 423:This article about 388:2017Entrp..19..381C 339:2003HMPS....1..262B 293:2017SHPMP..57...53G 128:Free molecular flow 96:Loschmidt's paradox 68:James Clerk Maxwell 37:in the writings of 60:in a small region 440: 439: 397:10.3390/e19080381 356:978-1-86094-347-8 100:after a collision 43:Tatiana Ehrenfest 495: 461: 454: 447: 419: 412: 402: 401: 399: 367: 361: 360: 319: 313: 312: 286: 266: 260: 227: 221: 220: 192: 186: 185: 183: 171: 165: 164: 144: 65: 59: 57: 50: 503: 502: 498: 497: 496: 494: 493: 492: 468: 467: 466: 465: 408: 406: 405: 369: 368: 364: 357: 328: 326: 321:L. Boltzmann, " 320: 316: 268: 267: 263: 257: : 21–37. 243: : 19–32. 228: 224: 194: 193: 189: 173: 172: 168: 161: 146: 145: 141: 136: 124: 108:Stosszahlansatz 75:BBGKY hierarchy 61: 55: 52: 46: 34:Stosszahlansatz 17: 12: 11: 5: 501: 499: 491: 490: 485: 480: 470: 469: 464: 463: 456: 449: 441: 438: 437: 420: 404: 403: 362: 355: 314: 261: 259: 258: 253:, 4th series, 244: 239:, 4th series, 222: 187: 166: 159: 138: 137: 135: 132: 131: 130: 123: 120: 15: 13: 10: 9: 6: 4: 3: 2: 500: 489: 486: 484: 481: 479: 476: 475: 473: 462: 457: 455: 450: 448: 443: 442: 436: 434: 430: 426: 421: 418: 414: 409: 398: 393: 389: 385: 381: 377: 373: 366: 363: 358: 352: 348: 344: 340: 336: 332: 324: 318: 315: 310: 306: 302: 298: 294: 290: 285: 280: 276: 272: 265: 262: 256: 252: 249: 245: 242: 238: 235: 231: 230: 226: 223: 218: 214: 210: 206: 202: 198: 191: 188: 182: 177: 170: 167: 162: 160:9780486495040 156: 152: 151: 143: 140: 133: 129: 126: 125: 121: 119: 117: 113: 109: 104: 101: 97: 93: 89: 84: 80: 76: 71: 69: 64: 58: 49: 44: 40: 36: 35: 31:(also called 30: 26: 22: 433:expanding it 422: 407: 379: 375: 365: 330: 317: 274: 270: 264: 254: 250: 240: 236: 225: 200: 196: 190: 169: 149: 142: 115: 107: 105: 99: 72: 62: 53: 47: 33: 32: 28: 18: 106:Though the 472:Categories 382:(8): 381. 284:1702.01411 134:References 277:: 53–65. 203:: 49–88. 181:0809.1304 88:Loschmidt 83:H-theorem 309:38272381 217:96568430 122:See also 384:Bibcode 376:Entropy 335:Bibcode 289:Bibcode 25:physics 19:In the 353:  307:  215:  157:  116:ansatz 427:is a 305:S2CID 279:arXiv 229:See: 213:S2CID 176:arXiv 66:. 56:' 429:stub 351:ISBN 155:ISBN 41:and 39:Paul 392:doi 343:doi 297:doi 205:doi 201:157 77:to 23:in 474:: 390:. 380:19 378:. 374:. 349:. 341:. 303:. 295:. 287:. 275:57 273:. 255:20 241:19 211:. 199:. 63:δr 27:, 460:e 453:t 446:v 435:. 400:. 394:: 386:: 359:. 345:: 337:: 311:. 299:: 291:: 281:: 219:. 207:: 184:. 178:: 163:. 54:v 48:v

Index

kinetic theory of gases
physics
Paul
Tatiana Ehrenfest
James Clerk Maxwell
BBGKY hierarchy
Boltzmann's equation
H-theorem
Loschmidt
irreversible process
Loschmidt's paradox
principle of maximum entropy
Free molecular flow
The Conceptual Foundations of the Statistical Approach in Mechanics
ISBN
9780486495040
arXiv
0809.1304
doi
10.1098/rstl.1867.0004
S2CID
96568430
"Illustrations of the dynamical theory of gases. Part I. On the motions and collisions of perfectly elastic spheres,"
"Illustrations of the dynamical theory of gases. Part II. On the process of diffusion of two or more kinds of moving particles among one another,"
arXiv
1702.01411
Bibcode
2017SHPMP..57...53G
doi
10.1016/j.shpsb.2017.01.001

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