{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T05:08:58Z","timestamp":1779167338874,"version":"3.51.4"},"reference-count":38,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Landauer principle motivates the definition of economic temperature as the monetary price of processing a bit irreversibly. No empirical test of this definition exists in transparent fee markets. This paper fills that gap using daily Bitcoin and Ethereum data, constructing canonical thermodynamic state variables and evaluating five diagnostic layers: state variable behavior, Maxwell-type integrability, Carnot-style efficiency bounds, nonlinear regime separation, and structural break sensitivity to protocol events. Bitcoin\u2019s log-temperature behaves as a persistent mean-reverting process with an AR(1) coefficient of 0.97 and a half-life of 21 days; Ethereum is highly persistent, with weaker formal evidence of stationarity than Bitcoin. Maxwell integrability is frequency-dependent: Bitcoin passes all four relations at monthly frequency, whereas Ethereum passes two of four. Carnot-style evidence is the strongest: realized fee extraction efficiency stays well below the implied bound, with daily compliance exceeding 97% on both chains. Structural breaks around Bitcoin ordinals, EIP-1559, the merge, and Shanghai confirm that protocol changes reorganize the temperature relation. The thermodynamic framework provides structure that standard fee market analysis does not, including a first principles efficiency bound and a state space coherence test. The findings provide partial, frequency-dependent, and chain-specific empirical support for a Landauer-based thermodynamic description of blockspace markets.<\/jats:p>","DOI":"10.3390\/e28050508","type":"journal-article","created":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T09:33:17Z","timestamp":1777627997000},"page":"508","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Landauer-Based Economic Temperature in Blockspace Markets: Evidence from Bitcoin and Ethereum"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-2228-713X","authenticated-orcid":false,"given":"Michael","family":"Zouari","sequence":"first","affiliation":[{"name":"Department of Economics and Business Administration, Ariel University, Ariel 40700, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ilan","family":"Alon","sequence":"additional","affiliation":[{"name":"Department of Economics and Business Administration, Ariel University, Ariel 40700, Israel"},{"name":"Department of Strategic Management, Institute of Strategy and Management, Corvinus University, F\u0151v\u00e1m t\u00e9r 8, 1093 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1471-3565","authenticated-orcid":false,"given":"Zeev","family":"Shtudiner","sequence":"additional","affiliation":[{"name":"Department of Economics and Business Administration, Ariel University, Ariel 40700, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1038\/nphys3230","article-title":"Thermodynamics of information","volume":"11","author":"Parrondo","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_2","first-page":"031015","article-title":"Thermodynamics with continuous information flow","volume":"4","author":"Horowitz","year":"2014","journal-title":"Phys. Rev. X"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"126001","DOI":"10.1088\/0034-4885\/75\/12\/126001","article-title":"Stochastic thermodynamics, fluctuation theorems and molecular machines","volume":"75","author":"Seifert","year":"2012","journal-title":"Rep. Prog. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"120604","DOI":"10.1103\/PhysRevLett.109.120604","article-title":"Thermodynamics of prediction","volume":"109","author":"Still","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.1103\/RevModPhys.81.1703","article-title":"Colloquium: Statistical mechanics of money, wealth, and income","volume":"81","author":"Yakovenko","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/S0378-4371(00)00205-3","article-title":"Wealth condensation in a simple model of economy","volume":"282","author":"Bouchaud","year":"2000","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1038\/4551181a","article-title":"Economics needs a scientific revolution","volume":"455","author":"Bouchaud","year":"2008","journal-title":"Nature"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bormashenko, E., and Shendrik, I. (2026). Econophysics and the Landauer principle: A redefinition of economic temperature. Entropy, 28.","DOI":"10.20944\/preprints202603.0238.v1"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bormashenko, E. (2024). Landauer bound in the context of minimal physical principles: Meaning, experimental verification, controversies and perspectives. Entropy, 26.","DOI":"10.20944\/preprints202404.0430.v1"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bormashenko, E. (2020). What is temperature? Modern outlook on the concept of temperature. Entropy, 22.","DOI":"10.20944\/preprints202011.0338.v1"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Bormashenko, E. (2019). Generalization of the Landauer principle for computing devices based on many-valued logic. Entropy, 21.","DOI":"10.20944\/preprints201910.0095.v1"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"P03025","DOI":"10.1088\/1742-5468\/2014\/03\/P03025","article-title":"Thermodynamic and logical reversibilities revisited","volume":"2014","author":"Sagawa","year":"2014","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.jfineco.2019.03.004","article-title":"From mining to markets: The evolution of bitcoin transaction fees","volume":"134","author":"Easley","year":"2019","journal-title":"J. Financ. Econ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3011","DOI":"10.1093\/restud\/rdab014","article-title":"Monopoly without a monopolist: An economic analysis of the Bitcoin payment system","volume":"88","author":"Huberman","year":"2021","journal-title":"Rev. Econ. Stud."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"101282","DOI":"10.1016\/j.intfin.2021.101282","article-title":"The market for bitcoin transactions","volume":"71","author":"Tsang","year":"2021","journal-title":"J. Int. Financ. Mark. Inst. Money"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1111\/jofi.13206","article-title":"Equilibrium Bitcoin pricing","volume":"78","author":"Biais","year":"2023","journal-title":"J. Financ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1156","DOI":"10.1093\/rfs\/hhaa075","article-title":"Blockchain without waste: Proof-of-stake","volume":"34","author":"Saleh","year":"2021","journal-title":"Rev. Financ. Stud."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Li, H., Xiao, Y., Polukarov, M., and Ventre, C. (2024). Thermodynamic analysis of financial markets: Measuring order book dynamics with temperature and entropy. Entropy, 26.","DOI":"10.3390\/e26010024"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhong, H., Liang, X., and Wang, Y. (2023). Transaction entropy: An alternative metric of market performance. Entropy, 25.","DOI":"10.3390\/e25081140"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1662","DOI":"10.1093\/rfs\/hhy095","article-title":"The blockchain folk theorem","volume":"32","author":"Biais","year":"2019","journal-title":"Rev. Financ. Stud."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1754","DOI":"10.1093\/rfs\/hhz007","article-title":"Blockchain disruption and smart contracts","volume":"32","author":"Cong","year":"2019","journal-title":"Rev. Financ. Stud."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.jfineco.2019.07.001","article-title":"Trading and arbitrage in cryptocurrency markets","volume":"135","author":"Makarov","year":"2020","journal-title":"J. Financ. Econ."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1093\/rfs\/hhaa089","article-title":"Tokenomics: Dynamic adoption and valuation","volume":"34","author":"Cong","year":"2021","journal-title":"Rev. Financ. Stud."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1016\/j.finmar.2013.06.004","article-title":"High-frequency trading","volume":"16","author":"Chordia","year":"2013","journal-title":"J. Financ. Mark."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1540-6261.2010.01624.x","article-title":"Does algorithmic trading improve liquidity?","volume":"66","author":"Hendershott","year":"2011","journal-title":"J. Financ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1016\/j.finmar.2013.06.006","article-title":"High frequency trading and the new market makers","volume":"16","author":"Menkveld","year":"2013","journal-title":"J. Financ. Mark."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2267","DOI":"10.1093\/rfs\/hhu032","article-title":"High-frequency trading and price discovery","volume":"27","author":"Brogaard","year":"2014","journal-title":"Rev. Financ. Stud."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"104507","DOI":"10.1016\/j.frl.2023.104507","article-title":"Blockchain transaction fee and Ethereum Merge","volume":"58","author":"Jain","year":"2023","journal-title":"Financ. Res. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"102338","DOI":"10.1016\/j.ribaf.2024.102338","article-title":"Bitcoin Ordinals: Determinants and impact on total transaction fees","volume":"70","author":"Bertucci","year":"2024","journal-title":"Res. Int. Bus. Financ."},{"key":"ref_30","first-page":"427","article-title":"Distribution of the estimators for autoregressive time series with a unit root","volume":"74","author":"Dickey","year":"1979","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/0304-4076(92)90104-Y","article-title":"Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?","volume":"54","author":"Kwiatkowski","year":"1992","journal-title":"J. Econom."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/jae.659","article-title":"Computation and analysis of multiple structural change models","volume":"18","author":"Bai","year":"2003","journal-title":"J. Appl. Econom."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"106570","DOI":"10.1016\/j.frl.2024.106570","article-title":"Transition to proof-of-stake and informed trading","volume":"72","author":"Choi","year":"2025","journal-title":"Financ. Res. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"112202","DOI":"10.1016\/j.econlet.2025.112202","article-title":"Ethereum\u2019s Merge: Market liquidity, efficiency and volatility in the Proof of Stake era","volume":"247","author":"Liu","year":"2025","journal-title":"Econ. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Daian, P., Goldfeder, S., Kell, T., Li, Y., Zhao, X., Bentov, I., Breidenbach, L., and Juels, A. (2020, January 18\u201321). Flash Boys 2.0: Frontrunning in decentralized exchanges, miner extractable value, and consensus instability. Proceedings of the 2020 IEEE Symposium on Security and Privacy (SP), San Francisco, CA, USA.","DOI":"10.1109\/SP40000.2020.00040"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Leonardos, S., Monnot, B., Reijsbergen, D., Skoulakis, E., and Piliouras, G. (2021). Dynamical analysis of the EIP-1559 Ethereum fee market. Proceedings of the 3rd ACM Conference on Advances in Financial Technologies (AFT\u201921), ACM.","DOI":"10.1145\/3479722.3480993"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1145\/3476436.3476445","article-title":"Transaction fee mechanism design","volume":"19","author":"Roughgarden","year":"2021","journal-title":"ACM SIGecom Exch."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2155","DOI":"10.1134\/S0005117921120079","article-title":"Comparison of banking and peer-to-peer lending risks","volume":"82","author":"Davydov","year":"2021","journal-title":"Autom. Remote Control"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/5\/508\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T04:16:35Z","timestamp":1779164195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/5\/508"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,1]]},"references-count":38,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["e28050508"],"URL":"https:\/\/doi.org\/10.3390\/e28050508","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,1]]}}}