{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:50:58Z","timestamp":1760151058146,"version":"build-2065373602"},"reference-count":66,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,28]],"date-time":"2022-01-28T00:00:00Z","timestamp":1643328000000},"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>This article investigates the spectral structure of the evolution operators associated with the statistical description of stochastic processes possessing finite propagation velocity. Generalized Poisson\u2013Kac processes and L\u00e9vy walks are explicitly considered as paradigmatic examples of regular and anomalous dynamics. A generic spectral feature of these processes is the lower boundedness of the real part of the eigenvalue spectrum that corresponds to an upper limit of the spectral dispersion curve, physically expressing the relaxation rate of a disturbance as a function of the wave vector. We also analyze Generalized Poisson\u2013Kac processes possessing a continuum of stochastic states parametrized with respect to the velocity. In this case, there is a critical value for the wave vector, above which the point spectrum ceases to exist, and the relaxation dynamics becomes controlled by the essential part of the spectrum. This model can be extended to the quantum case, and in fact, it represents a simple and clear example of a sub-quantum dynamics with hidden variables.<\/jats:p>","DOI":"10.3390\/e24020201","type":"journal-article","created":{"date-parts":[[2022,1,29]],"date-time":"2022-01-29T01:41:59Z","timestamp":1643420519000},"page":"201","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Spectral Properties of Stochastic Processes Possessing Finite Propagation Velocity"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5875-0160","authenticated-orcid":false,"given":"Massimiliano","family":"Giona","sequence":"first","affiliation":[{"name":"Dipartimento Ingegneria Chimica Materiali Ambiente, La Sapienza Universit\u00e0 di Roma, Via Eudossiana 18, 00184 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Cairoli","sequence":"additional","affiliation":[{"name":"The Francis Crick Institute, 1 Midland Road, London NW1 1AT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Davide","family":"Cocco","sequence":"additional","affiliation":[{"name":"Dipartimento SBAI, La Sapienza Universit\u00e0 di Roma, Via Antonio Scarpa 16, 00161 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3811-3070","authenticated-orcid":false,"given":"Rainer","family":"Klages","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Klages, R., Just, W., and Jarzynski, C. 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