{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T16:32:21Z","timestamp":1774542741844,"version":"3.50.1"},"reference-count":79,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,30]],"date-time":"2024-12-30T00:00:00Z","timestamp":1735516800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Los Alamos National Laboratory (LANL) Directed Research and Development funds (LDRD)"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A stochastic energetics framework is applied to examine how periodically shifting the frequency of a time-dependent oscillating temperature gradient affects heat transport in a nanoscale molecular model. We specifically examine the effects that frequency switching, i.e., instantaneously changing the oscillation frequency of the temperature gradient, has on the shape of the heat transport hysteresis curves generated by a particle connected to two thermal baths, each with a temperature that is oscillating in time. Analytical expressions are derived for the energy fluxes in\/out of the system and the baths, with excellent agreement observed between the analytical expressions and the results from nonequilibrium molecular dynamics simulations. We find that the shape of the heat transport hysteresis curves can be significantly altered by shifting the frequency between fast and slow oscillation regimes. We also observe the emergence of features in the hysteresis curves such as pinched loops and complex multi-loop patterns due to the frequency shifting. The presented results have implications in the design of thermal neuromorphic devices such as thermal memristors and thermal memcapacitors.<\/jats:p>","DOI":"10.3390\/e27010018","type":"journal-article","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T07:34:19Z","timestamp":1735630459000},"page":"18","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Heat Transport Hysteresis Generated Through Frequency Switching of a Time-Dependent Temperature Gradient"],"prefix":"10.3390","volume":"27","author":[{"given":"Renai","family":"Chen","sequence":"first","affiliation":[{"name":"Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}]},{"given":"Galen T.","family":"Craven","sequence":"additional","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"065002","DOI":"10.1063\/1.4985055","article-title":"Thermal memristor and neuromorphic networks for manipulating heat flow","volume":"7","year":"2017","journal-title":"AIP Adv."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"025901","DOI":"10.1103\/PhysRevLett.123.025901","article-title":"Radiative Thermal Memristor","volume":"123","author":"Ezzahri","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"024148","DOI":"10.1103\/PhysRevE.108.024148","article-title":"Energy transport between heat baths with oscillating temperatures","volume":"108","author":"Chen","year":"2023","journal-title":"Phys. Rev. E"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1103\/PhysRev.114.1192","article-title":"Stationary Nonequilibrium Gibbsian Ensembles","volume":"114","author":"Lebowitz","year":"1959","journal-title":"Phys. Rev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1063\/1.1705319","article-title":"Properties of a Harmonic Crystal in a Stationary Nonequilibrium State","volume":"8","author":"Rieder","year":"1967","journal-title":"J. Math. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1063\/1.1665794","article-title":"Heat Flow in Regular and Disordered Harmonic Chains","volume":"12","author":"Casher","year":"1971","journal-title":"J. Math. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1063\/1.1524305","article-title":"Nanoscale thermal transport","volume":"93","author":"Cahill","year":"2003","journal-title":"J. Appl. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"034301","DOI":"10.1103\/PhysRevLett.94.034301","article-title":"Spin-Boson Thermal Rectifier","volume":"94","author":"Segal","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1146\/annurev-physchem-040215-112103","article-title":"Vibrational Heat Transport in Molecular Junctions","volume":"67","author":"Segal","year":"2016","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"155312","DOI":"10.1103\/PhysRevB.75.155312","article-title":"Heat conduction in molecular transport junctions","volume":"75","author":"Galperin","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"214303","DOI":"10.1103\/PhysRevLett.108.214303","article-title":"Heat Flux Manipulation with Engineered Thermal Materials","volume":"108","author":"Narayana","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1038\/nature12608","article-title":"Sound and heat revolutions in phononics","volume":"503","author":"Maldovan","year":"2013","journal-title":"Nature"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1146\/annurev.physchem.59.032607.093606","article-title":"Energy Flow in Proteins","volume":"59","author":"Leitner","year":"2008","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"12820","DOI":"10.1021\/jp402012z","article-title":"Thermal Boundary Conductance and Thermal Rectification in Molecules","volume":"117","author":"Leitner","year":"2013","journal-title":"J. Phys. Chem. B"},{"key":"ref_15","first-page":"031019","article-title":"Thermodynamics of Micro- and Nano-Systems Driven by Periodic Temperature Variations","volume":"5","author":"Brandner","year":"2015","journal-title":"Phys. Rev. X"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1103\/RevModPhys.84.1045","article-title":"Colloquium: Phononics: Manipulating heat flow with electronic analogs and beyond","volume":"84","author":"Li","year":"2012","journal-title":"Rev. Mod. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1103\/RevModPhys.83.131","article-title":"Colloquium: Heat flow and thermoelectricity in atomic and molecular junctions","volume":"83","author":"Dubi","year":"2011","journal-title":"Rev. Mod. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"201304","DOI":"10.1103\/PhysRevB.88.201304","article-title":"Dynamic thermoelectric and heat transport in mesoscopic capacitors","volume":"88","author":"Lim","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"9421","DOI":"10.1073\/pnas.1609141113","article-title":"Electron transfer across a thermal gradient","volume":"113","author":"Craven","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"062121","DOI":"10.1103\/PhysRevE.103.062121","article-title":"Effects of interplay between disorder and anharmonicity on heat conduction","volume":"103","author":"Zhu","year":"2021","journal-title":"Phys. Rev. E"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"L100102","DOI":"10.1103\/PhysRevB.106.L100102","article-title":"Net heat current at zero mean temperature gradient","volume":"106","author":"Anufriev","year":"2022","journal-title":"Phys. Rev. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"9834","DOI":"10.1021\/acs.jpclett.3c02367","article-title":"Heat Transfer Enhancement in Tree-Structured Polymer Linked Gold Nanoparticle Networks","volume":"14","author":"Wei","year":"2023","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"144113","DOI":"10.1063\/5.0022423","article-title":"Stochastic simulation of nonequilibrium heat conduction in extended molecular junctions","volume":"153","author":"Sharony","year":"2020","journal-title":"J. Chem. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"054221","DOI":"10.1103\/PhysRevE.108.054221","article-title":"Nonequilibrium thermal rectification at the junction of harmonic chains","volume":"108","author":"Dmitriev","year":"2023","journal-title":"Phys. Rev. E"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2204781","DOI":"10.1002\/adfm.202204781","article-title":"Bipolar Junction Transistor Exhibiting Excellent Output Characteristics with a Prompt Response against the Selective Protein","volume":"32","author":"Dastgeer","year":"2022","journal-title":"Adv. Funct. Mater."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"109106","DOI":"10.1016\/j.nanoen.2023.109106","article-title":"Atomically engineered, high-speed non-volatile flash memory device exhibiting multibit data storage operations","volume":"119","author":"Dastgeer","year":"2024","journal-title":"Nano Energy"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"194305","DOI":"10.1063\/5.0204819","article-title":"Molecular heat transport across a time-periodic temperature gradient","volume":"160","author":"Chen","year":"2024","journal-title":"J. Chem. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"174306","DOI":"10.1063\/5.0144248","article-title":"Electron hopping heat transport in molecules","volume":"158","author":"Craven","year":"2023","journal-title":"J. Chem. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"194704","DOI":"10.1063\/1.1900063","article-title":"Heat rectification in molecular junctions","volume":"122","author":"Segal","year":"2005","journal-title":"J. Chem. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"085424","DOI":"10.1103\/PhysRevB.76.085424","article-title":"Thermal rectification in carbon nanotube intramolecular junctions: Molecular dynamics calculations","volume":"76","author":"Wu","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"105901","DOI":"10.1103\/PhysRevLett.100.105901","article-title":"Single Mode Heat Rectifier: Controlling Energy Flow Between Electronic Conductors","volume":"100","author":"Segal","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"095503","DOI":"10.1103\/PhysRevLett.102.095503","article-title":"Sufficient Conditions for Thermal Rectification in Hybrid Quantum Structures","volume":"102","author":"Wu","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"247704","DOI":"10.1103\/PhysRevLett.121.247704","article-title":"Electron-Transfer-Induced Thermal and Thermoelectric Rectification","volume":"121","author":"Craven","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"012134","DOI":"10.1103\/PhysRevE.103.012134","article-title":"Heat rectification with a minimal model of two harmonic oscillators","volume":"103","author":"Pons","year":"2021","journal-title":"Phys. Rev. E"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"205321","DOI":"10.1103\/PhysRevB.81.205321","article-title":"Thermoelectric and thermal rectification properties of quantum dot junctions","volume":"81","author":"Kuo","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"184301","DOI":"10.1103\/PhysRevLett.93.184301","article-title":"Thermal Diode: Rectification of Heat Flux","volume":"93","author":"Li","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"060201","DOI":"10.1103\/PhysRevE.74.060201","article-title":"Thermal rectifying effect in macroscopic size","volume":"74","author":"Hu","year":"2006","journal-title":"Phys. Rev. E"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1016\/j.ijthermalsci.2010.12.004","article-title":"A review of thermal rectification observations and models in solid materials","volume":"50","author":"Roberts","year":"2011","journal-title":"Int. J. Therm. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1038\/nnano.2015.11","article-title":"Rectification of electronic heat current by a hybrid thermal diode","volume":"10","author":"Fornieri","year":"2015","journal-title":"Nat. Nanotechnol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"100941","DOI":"10.1016\/j.mtphys.2022.100941","article-title":"Progress in thermal rectification due to heat conduction in micro\/nano solids","volume":"30","author":"Zhao","year":"2023","journal-title":"Mater. Today Phys."},{"key":"ref_41","first-page":"025302","article-title":"Thermal rectification in mass-asymmetric one-dimensional anharmonic oscillator lattices with and without a ballistic spacer","volume":"36","year":"2023","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"143501","DOI":"10.1063\/1.2191730","article-title":"Negative differential thermal resistance and thermal transistor","volume":"88","author":"Li","year":"2006","journal-title":"Appl. Phys. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"044301","DOI":"10.1103\/PhysRevLett.112.044301","article-title":"Near-Field Thermal Transistor","volume":"112","author":"Biehs","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"200601","DOI":"10.1103\/PhysRevLett.116.200601","article-title":"Quantum Thermal Transistor","volume":"116","author":"Joulain","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"13172","DOI":"10.1039\/C7CP02445B","article-title":"Microscale solid-state thermal diodes enabling ambient temperature thermal circuits for energy applications","volume":"19","author":"Wang","year":"2017","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"092305","DOI":"10.1063\/1.4971293","article-title":"Electron transfer at thermally heterogeneous molecule-metal interfaces","volume":"146","author":"Craven","year":"2017","journal-title":"J. Chem. Phys."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Odebowale, A.A., Berhe, A.M., Hattori, H.T., and Miroshnichenko, A.E. (2024). Modeling and Analysis of a Radiative Thermal Memristor. Appl. Sci., 14.","DOI":"10.3390\/app14062633"},{"key":"ref_48","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_49","first-page":"155","article-title":"Stochastic thermodynamics: A brief introduction","volume":"Volume 184","year":"2013","journal-title":"Physics of Complex Colloids"},{"key":"ref_50","first-page":"57","article-title":"Brownian motors: Noisy transport far from equilibrium","volume":"361","author":"Reimann","year":"2002","journal-title":"Phys. Rev."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1007\/BF01027298","article-title":"Generalized Langevin equations with time-dependent temperature","volume":"61","author":"Brey","year":"1990","journal-title":"J. Stat. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"244506","DOI":"10.1063\/1.2743032","article-title":"Ontology of temperature in nonequilibrium systems","volume":"126","author":"Popov","year":"2007","journal-title":"J. Chem. Phys."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"032145","DOI":"10.1103\/PhysRevE.88.032145","article-title":"Temperature-driven irreversible generalized Langevin equation can capture the nonequilibrium dynamics of two dissipated coupled oscillators","volume":"88","author":"Popov","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"042108","DOI":"10.1103\/PhysRevE.92.042108","article-title":"Stochastic entropy production arising from nonstationary thermal transport","volume":"92","author":"Ford","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"062134","DOI":"10.1103\/PhysRevE.93.062134","article-title":"Periodic thermodynamics of open quantum systems","volume":"93","author":"Brandner","year":"2016","journal-title":"Phys. Rev. E"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"062143","DOI":"10.1103\/PhysRevE.103.062143","article-title":"Oscillating states of periodically driven anharmonic Langevin systems","volume":"103","author":"Awasthi","year":"2021","journal-title":"Phys. Rev. E"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"043112","DOI":"10.1103\/PhysRevResearch.4.043112","article-title":"Effective temperature pulses in open quantum systems","volume":"4","author":"Portugal","year":"2022","journal-title":"Phys. Rev. Res."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"064127","DOI":"10.1103\/PhysRevE.106.064127","article-title":"Temperature and friction fluctuations inside a harmonic potential","volume":"106","author":"Stanislavsky","year":"2022","journal-title":"Phys. Rev. E"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"042209","DOI":"10.1103\/PhysRevE.101.042209","article-title":"Ballistic resonance and thermalization in the Fermi-Pasta-Ulam-Tsingou chain at finite temperature","volume":"101","author":"Kuzkin","year":"2020","journal-title":"Phys. Rev. E"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"405201","DOI":"10.1088\/1361-648X\/ad5d40","article-title":"The effect of temperature oscillations on energy storage rectification in harmonic systems","volume":"36","author":"Chen","year":"2024","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_61","unstructured":"Bernardo, M., Budd, C., Champneys, A.R., and Kowalczyk, P. (2008). Piecewise-Smooth Dynamical Systems: Theory and Applications, Springer Science & Business Media."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"105950","DOI":"10.1016\/j.cnsns.2021.105950","article-title":"Ageing of an oscillator due to frequency switching","volume":"102","author":"Bonet","year":"2021","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"107032","DOI":"10.1016\/j.cnsns.2022.107032","article-title":"Novel slow\u2013fast behaviour in an oscillator driven by a frequency-switching force","volume":"118","author":"Bonet","year":"2023","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"113270","DOI":"10.1016\/j.chaos.2023.113270","article-title":"Sliding fast\u2013slow dynamics in the slowly forced Duffing system with frequency switching","volume":"169","author":"Han","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"19013","DOI":"10.1007\/s11071-024-10047-6","article-title":"A novel route to bursting by frequency switching in the slowly forced Duffing system","volume":"112","author":"Jiang","year":"2024","journal-title":"Nonlinear Dyn."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1143\/PTPS.130.17","article-title":"Langevin Equation and Thermodynamics","volume":"130","author":"Sekimoto","year":"1998","journal-title":"Prog. Theor. Phys. Supp."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"104103","DOI":"10.1063\/1.5045361","article-title":"Upside\/Downside statistical mechanics of nonequilibrium Brownian motion. II. Heat transport and energy partitioning of a free particle","volume":"149","author":"Craven","year":"2018","journal-title":"J. Chem. Phys."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"044101","DOI":"10.1063\/1.5007854","article-title":"Upside\/Downside statistical mechanics of nonequilibrium Brownian motion. I. Distributions, moments, and correlation functions of a free particle","volume":"148","author":"Craven","year":"2018","journal-title":"J. Chem. Phys."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"090601","DOI":"10.1103\/PhysRevLett.121.090601","article-title":"Arcsine Laws in Stochastic Thermodynamics","volume":"121","author":"Barato","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"021108","DOI":"10.1103\/PhysRevE.85.021108","article-title":"Heat and work fluctuations for a harmonic oscillator","volume":"85","author":"Sabhapandit","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.physa.2014.06.002","article-title":"Heat transport and current fluctuations in harmonic crystals","volume":"418","author":"Dhar","year":"2015","journal-title":"Phys. A"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"1568","DOI":"10.1126\/science.1137149","article-title":"Thermoelectricity in Molecular Junctions","volume":"315","author":"Reddy","year":"2007","journal-title":"Science"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"8838","DOI":"10.1021\/ja202178k","article-title":"Effect of Length and Contact Chemistry on the Electronic Structure and Thermoelectric Properties of Molecular Junctions","volume":"133","author":"Tan","year":"2011","journal-title":"J. Am. Chem. Soc."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1038\/nature12183","article-title":"Heat dissipation in atomic-scale junctions","volume":"498","author":"Lee","year":"2013","journal-title":"Nature"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1038\/nnano.2014.209","article-title":"Electrostatic control of thermoelectricity in molecular junctions","volume":"9","author":"Kim","year":"2014","journal-title":"Nat. Nanotech."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1038\/nnano.2015.97","article-title":"Single-molecule diodes with high rectification ratios through environmental control","volume":"10","author":"Capozzi","year":"2015","journal-title":"Nat. Nanotech."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1038\/s41586-019-1420-z","article-title":"Thermal conductance of single-molecule junctions","volume":"572","author":"Cui","year":"2019","journal-title":"Nature"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"7614","DOI":"10.1021\/acs.nanolett.9b02089","article-title":"Thermal Transport through Single-Molecule Junctions","volume":"19","author":"Mosso","year":"2019","journal-title":"Nano Lett."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"2632","DOI":"10.1021\/acs.jpcb.0c00059","article-title":"Energy, Work, Entropy, and Heat Balance in Marcus Molecular Junctions","volume":"124","author":"Zimbovskaya","year":"2020","journal-title":"J. Phys. Chem. B"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/1\/18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:56:21Z","timestamp":1760115381000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/1\/18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,30]]},"references-count":79,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["e27010018"],"URL":"https:\/\/doi.org\/10.3390\/e27010018","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,30]]}}}