{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:41:56Z","timestamp":1760244116996,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2004,3,23]],"date-time":"2004-03-23T00:00:00Z","timestamp":1080000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Using an isolated measurement process, I've calculated the effect measurement has on entropy for the multi-cylinder Szilard engine. This calculation shows that the system of cylinders possesses an entropy associated with cylinder total energy states, and that it records information transferred at measurement. Contrary to other's results, I've found that the apparatus loses entropy due to measurement. The Second Law of Thermodynamics may be preserved if Maxwell's demon gains entropy moving the engine partition.<\/jats:p>","DOI":"10.3390\/e6010102","type":"journal-article","created":{"date-parts":[[2008,10,25]],"date-time":"2008-10-25T13:44:42Z","timestamp":1224942282000},"page":"102-115","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Modified Szilard's Engine: Measurement, Information, and Maxwell's Demon"],"prefix":"10.3390","volume":"6","author":[{"given":"Michael","family":"Devereux","sequence":"first","affiliation":[{"name":"Los Alamos Economic Development Corporation, 127 Eastgate Dr., Los Alamos, NM 87544, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2004,3,23]]},"reference":[{"unstructured":"Maxwell, J.C. (1871). Theory of Heat, Longmans, Green, and Co.. Chp. 12.","key":"ref_1"},{"doi-asserted-by":"crossref","unstructured":"Szilard\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t              L.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          Uber die Entropieverminderung in einnem thermodynamischen System bei Eingriffen intelligenter Wesen\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          Z. f. Physik.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          1929\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          53\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          840\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          856\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          10.1007\/BF01341281\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t        \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          English translation in \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t        \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  Maxwell\u2019s Demon: Entropy, Information, Computing\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t              Leff\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t              Harvey S.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t              Rex\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t              Andrew F.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  Princeton University Press\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  Princeton\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  1992\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t  124","key":"ref_2","DOI":"10.1007\/BF01341281"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1007\/BF00670091","article-title":"Keeping the Entropy of Measurement: Szilard Revisisted","volume":"26","author":"Lubkin","year":"1987","journal-title":"Int. J. Theor. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/BF02058888","article-title":"Maxwell\u2019s Demon and the Entropy Cost of Information","volume":"26","author":"Fahn","year":"1996","journal-title":"Found. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1007\/BF02055259","article-title":"A Qantum-Mechanical Treatment of Szialrd\u2019s Engine: Implications for the Entropy of Information","volume":"25","author":"Biedenharn","year":"1995","journal-title":"Found. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1119\/1.17749","article-title":"Entropy of measurement and erasure: Szilard\u2019s membrane model revisited","volume":"62","author":"Leff","year":"1994","journal-title":"Am. J. Phys."},{"unstructured":"Moore, G. T., and Scully, M. O. (1984). Frontiers of Nonequilibrium Statistical Physics, Plenum Press.","key":"ref_7"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1147\/rd.53.0183","article-title":"Irreversibility and heat generation in the computing process","volume":"5","author":"Landauer","year":"1961","journal-title":"IBM J. Res. Dev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1007\/BF02084158","article-title":"The thermodynamics of computation\u2014a review","volume":"21","author":"Bennett","year":"1982","journal-title":"Int. J. Theor. Phys."},{"unstructured":"Knott, C. G. (1911). Life and Scientific Work of Peter Guthrie Tait, Cambridge University Press.","key":"ref_10"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1038\/009441c0","article-title":"The Kinetic Theory of the Dissipation of Energy","volume":"9","author":"Thompson","year":"1874","journal-title":"Nature"},{"unstructured":"Ref. [2], p. 127.","key":"ref_12"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1038\/scientificamerican1187-108","article-title":"Demons, engines and the second law","volume":"257","author":"Bennett","year":"1987","journal-title":"Sci. Am."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1103\/PhysRevLett.52.232","article-title":"Dissipation in computation","volume":"52","author":"Porod","year":"1984","journal-title":"Phys. Rev. Lett."},{"unstructured":"Moreover, it is obvious, irrespective of whatever mathematical formalism is used for the calculation, that the cylinders of the multi-cylinder Szilard engine possess entropy. The cylinders are in thermodynamic equilibrium with the enclosed gas molecules; there is a probability distribution of the total energy states of the cylinders. No entropy balance determination, including Zurek\u2019s, is valid if it neglects the entropy of the cylinders.","key":"ref_15"},{"unstructured":"Leff, Harvey S., and Rex, Andrew F. (1992). Maxwell\u2019s Demon: Entropy, Information, Computing, Princeton University Press.","key":"ref_16"},{"unstructured":"Zurek showed in Ref. [7] that it is the measurement, not partition insertion by itself, which confines the gas molecules\u2019 wavefunction to approximately half the cylinder volume. I believe that a collision between the gas and the cylinder captures the molecule on one side of the cylinder, and sustains the claim that a collision is indeed a measurement.","key":"ref_17"},{"unstructured":"See Maxwell\u2019s letter to Tait, in Ref. [10]. \u201cConcerning Demons\u2026.What was their chief end? To show that the 2nd Law of Thermodynamics has only a statistical certainty.\u201d","key":"ref_18"},{"unstructured":"Implying that both halves of every cylinder, separated by the thin insulating layer, are initially at temperature T0.","key":"ref_19"},{"unstructured":"It is particularly noteworthy that the information specifying either right or left confinement for each individual molecule following partition and measurement, necessary for engine operation, entails no associated entropy. If the value of a physical characteristic may be assigned to each constituent of a thermodynamic system, the corresponding state of that system is completely determined, and its associated entropy is therefore zero. (As, for example, specifying the momentum of each molecule of an ideal gas.) There is unit probability that the system occupies that particular state. This fact, I believe, has hitherto remained largely unappreciated in discussions of Szilard\u2019s engine. Calculation will show that the collection of cylinders does, nevertheless, experience an entropy shift following partition and measurement.","key":"ref_20"},{"unstructured":"Both halves of the cylinder at temperature T0.","key":"ref_21"},{"unstructured":"There is no assumption that the partition closes instantaneously. As usual for the Szilard engine, the partition is considered essentially massless. We require that it have so little mass that it can be closed in a time short relative to the average time between collisions of a gas molecule with the cylinder.","key":"ref_22"},{"unstructured":"Zurek showed in Ref. [7] that it is the measurement, the molecule-cylinder collision in this case, not partition itself, which confines the molecule to half the original volume. Thus, the probable molecule energy before the collision is a function of the quantum energy states within the whole cylinder, and the molecule\u2019s probable energy after the collision depends on the quantum energy levels for a partitioned cylinder.","key":"ref_23"},{"unstructured":"Certainly, a measurement of a physical characteristic of the entire system, such as volume, or temperature, may result in an entropy change. The entropy shift we have calculated actually indicates that all molecules are now confined to half their original volume, irrespective of whether it is the right or left side of the cylinder; that the moment of inertia of every cylinder plus molecule is now altered.","key":"ref_24"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1119\/1.18030","article-title":"Thermodynamic insights from a one-particle gas","volume":"63","author":"Leff","year":"1995","journal-title":"Am. J. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1209\/epl\/i1996-00382-3","article-title":"Szilard\u2019s heat engine","volume":"33","author":"Magnasco","year":"1996","journal-title":"Europhys. Lett."},{"unstructured":"Facilitated by the division of the cylinder into right and left halves by the thin sheet of thermal insulation.","key":"ref_27"},{"unstructured":"Ref. [7], p.158.","key":"ref_28"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"0623141","DOI":"10.1103\/PhysRevA.61.062314","article-title":"Information Erasure","volume":"61","author":"Piechocinska","year":"2000","journal-title":"Phys. Rev. A."},{"unstructured":"Zurek, W. H. Algorithmic Randomness, Physical Entropy, Measurements, and the Demon of Choice, In electronic archives at http:\/\/xxx.lanl.gov\/e-print\/quant-ph\/9807007.","key":"ref_30"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/6\/1\/102\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:26:15Z","timestamp":1760221575000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/6\/1\/102"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,3,23]]},"references-count":30,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,3]]}},"alternative-id":["e6010102"],"URL":"https:\/\/doi.org\/10.3390\/e6010102","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2004,3,23]]}}}