熵

一杯凍檸水嘅冰溶化，冰當中嘅 H₂O 分子變成水，並且散開。

唔好同資訊熵搞亂。

熵（粵拼：soeng¹；英文：entropy）係統計力學同熱力學等領域常用嘅一個概念，係一個熱力學系統具有嘅外延性質（外延性質係會同個系統嘅大細成比例嘅物理性質）。考慮 $\Omega$ 呢個數值：是但搵個熱力學系統，佢會有一啲宏觀性質（例如溫度、壓力等），而個系統會有若干個可能嘅微狀態（microstate；「粒子 A 喺位置 X 而粒子 B 喺位置 Y...」、「粒子 A 喺位置 Y 而粒子 B 喺位置 X...」等等），能夠同個系統啲宏觀性質吻合嘅微狀態數量就係 $\Omega$ 咁多個；熵係 $\Omega$ 嘅函數，即係話熵反映咗「已知個系統嘅宏觀性質如此，個系統有幾多個可能嘅微狀態」。假設每個微狀態都一樣咁有可能發生（概率一樣），個系統嘅熵可以用以下呢條式計出嚟^[1]^[2]：

S=k_{\mathrm {B} }\ln \Omega .

當中 $k B$ 係波茲曼常數（Boltzmann constant）^[3]。

喺實際應用上， $\Omega$ 嘅數值通常都極之大：根據估計，一嚿喺室溫同大氣壓力之下、容量 20 公升嘅氣體總共有大約 $N \approx &000000082000-80-66.000000 6 \times 1023$ 咁多粒氣體分子（阿伏加德羅常數；Avogadro number），而呢嚿氣體嘅 $\Omega$ 數值（ $\Omega$ 反映「已知呢嚿氣體有 $N \approx &000000082000-80-66.000000 6 \times 1023$ 粒分子，可能嘅微狀態數量」）會更加大^[3]。

熱力學第二定律[編輯]

睇埋：熱力學第二定律

根據熱力學第二定律（The second law of thermodynamics），一個封閉系統（closed system）當中嘅熵永遠唔會跌，只有可能維持不變或者升。熱力學第二定律意味住，搵個封閉系統，隨住時間過去，個系統內部嘅粒子同能量頂櫳維持唔郁，而喺現實多數會慢慢走位（可能嘅微狀態數量上升），會漸漸趨向熱力學平衡（thermodynamic equilibrium）－熵數值最大化嘅狀態。好似生物等嘅非封閉系統（會同周圍環境傳能量）可以內部熵下降，但噉做實會引致佢周圍環境嘅熵升，而且升至少同一樣咁多。因為噉，宇宙嘅總熵依然會升^[4]。

順帶一提，如果宇宙最後真係完全變成熱力學平衡，根據物理學家計算，宇宙最後會變成溫度分佈完全平均，而且溫度接近絕對零度（攝氏零下 273.15 度）嘅空間，唔會再有任何作功，更加唔會有生命－而呢個情況就係假想中嘅熱寂（heat death）^[5]。

同資訊嘅啦掕[編輯]

睇埋：資訊理論

熵仲同資訊有住密切嘅啦掕：熵由帶隨機性嘅微狀態數量決定，所以熵會反映「知道咗個系統嘅宏觀性質，需要幾多資訊先可以講明個系統處於乜嘢物理狀態」；因為呢個緣故，外行人會話熵表達咗個系統有幾「亂」－一個系統嘅熵愈高，就表示觀察者對個系統知道得愈少（有愈多不確定嘅可能性），所以就愈「亂」。而對物理意義上嘅熵嘅考量的確同資訊理論（information theory）有關（不過資訊理論當中講嘅「熵」係一個同物理熵唔同嘅概念）^[6]^[7]。

睇埋[編輯]

參考[編輯]

Adam, Gerhard; Otto Hittmair (1992). Wärmetheorie. Vieweg, Braunschweig. ISBN 978-3-528-33311-9.
Atkins, Peter; Julio De Paula (2006). Physical Chemistry (8th ed.). Oxford University Press. ISBN 978-0-19-870072-2.
Baierlein, Ralph (2003). Thermal Physics. Cambridge University Press. ISBN 978-0-521-65838-6.
Ben-Naim, Arieh (2007). Entropy Demystified. World Scientific. ISBN 978-981-270-055-1.
Callen, Herbert, B (2001). Thermodynamics and an Introduction to Thermostatistics (2nd ed.). John Wiley and Sons. ISBN 978-0-471-86256-7.
Chang, Raymond (1998). Chemistry (6th ed.). New York: McGraw Hill. ISBN 978-0-07-115221-1.
Cutnell, John, D.; Johnson, Kenneth, J. (1998). Physics (4th ed.). John Wiley and Sons, Inc. ISBN 978-0-471-19113-1.
Dugdale, J. S. (1996). Entropy and its Physical Meaning (2nd ed.). Taylor and Francis (UK); CRC (US). ISBN 978-0-7484-0569-5.
Fermi, Enrico (1937). Thermodynamics. Prentice Hall. ISBN 978-0-486-60361-2.
Goldstein, Martin; Inge, F (1993). The Refrigerator and the Universe. Harvard University Press. ISBN 978-0-674-75325-9.
Gyftopoulos, E.P.; G.P. Beretta (2010). Thermodynamics. Foundations and Applications. Dover. ISBN 978-0-486-43932-7.
Haddad, Wassim M.; Chellaboina, VijaySekhar; Nersesov, Sergey G. (2005). Thermodynamics – A Dynamical Systems Approach. Princeton University Press. ISBN 978-0-691-12327-1.
Kroemer, Herbert; Charles Kittel (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 978-0-7167-1088-2.
Müller-Kirsten, Harald J. W. (2013). Basics of Statistical Physics (2nd ed.). Singapore: World Scientific. ISBN 978-981-4449-53-3.
Penrose, Roger (2005). The Road to Reality: A Complete Guide to the Laws of the Universe. New York: A. A. Knopf. ISBN 978-0-679-45443-4.
Reif, F. (1965). Fundamentals of statistical and thermal physics. McGraw-Hill. ISBN 978-0-07-051800-1.
Schroeder, Daniel V. (2000). Introduction to Thermal Physics. New York: Addison Wesley Longman. ISBN 978-0-201-38027-9.
Serway, Raymond, A. (1992). Physics for Scientists and Engineers. Saunders Golden Subburst Series. ISBN 978-0-03-096026-0.
Spirax-Sarco Limited, Entropy – A Basic Understanding A primer on entropy tables for steam engineering.
von Baeyer; Hans Christian (1998). Maxwell's Demon: Why Warmth Disperses and Time Passes. Random House. ISBN 978-0-679-43342-2.

攷[編輯]

↑ Ligrone, Roberto (2019). "Glossary". Biological Innovations that Built the World: A Four-billion-year Journey through Life & Earth History. Entropy. Springer. p. 478.
↑ Baierlein, Ralph (2003). Thermal Physics. Cambridge University Press.
↑ ^3.0 ^3.1 Richard Feynman (1970). The Feynman Lectures on Physics Vol I. Addison Wesley Longman.
↑ Zohuri, Bahman (2016). Dimensional Analysis Beyond the Pi Theorem. Springer. p. 111.
↑ Adams, Fred C.; Laughlin, Gregory (1997). "A dying universe: the long-term fate and evolution of astrophysical objects". Reviews of Modern Physics. 69 (2): 337–72.
↑ Rietman, Edward A.; Tuszynski, Jack A. (2017). "Thermodynamics & Cancer Dormancy: A Perspective". In Wang, Yuzhuo; Crea, Francesco (eds.). Tumor Dormancy & Recurrence (Cancer Drug Discovery and Development). Introduction: Entropy & Information. Humana Press. p. 63.
↑ Brooks, D. R., Collier, J., Maurer, B. A., Smith, J. D., & Wiley, E. O. (1989). Entropy and information in evolving biological systems. Biology and Philosophy, 4(4), 407-432.

拎[編輯]

Entropy and the Second Law of Thermodynamics – an A-level physics lecture with detailed derivation of entropy based on Carnot cycle.

[1] Ligrone, Roberto (2019). "Glossary". Biological Innovations that Built the World: A Four-billion-year Journey through Life & Earth History. Entropy. Springer. p. 478.

[baierlein2003-2] Baierlein, Ralph (2003). Thermal Physics. Cambridge University Press.

[feynman1970-3] 3.0 ^3.1 Richard Feynman (1970). The Feynman Lectures on Physics Vol I. Addison Wesley Longman.

[4] Zohuri, Bahman (2016). Dimensional Analysis Beyond the Pi Theorem. Springer. p. 111.

[5] Adams, Fred C.; Laughlin, Gregory (1997). "A dying universe: the long-term fate and evolution of astrophysical objects". Reviews of Modern Physics. 69 (2): 337–72.

[6] Rietman, Edward A.; Tuszynski, Jack A. (2017). "Thermodynamics & Cancer Dormancy: A Perspective". In Wang, Yuzhuo; Crea, Francesco (eds.). Tumor Dormancy & Recurrence (Cancer Drug Discovery and Development). Introduction: Entropy & Information. Humana Press. p. 63.

[brooks1989-7] Brooks, D. R., Collier, J., Maurer, B. A., Smith, J. D., & Wiley, E. O. (1989). Entropy and information in evolving biological systems. Biology and Philosophy, 4(4), 407-432.

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