Non-Equilibrium Thermodynamics of Heat Transport in Superlattices, Graded Systems, and Thermal Metamaterials with Defects.

In this review, we discuss a nonequilibrium thermodynamic theory for heat transport in superlattices, graded systems, and thermal metamaterials with defects. The aim is to provide researchers in nonequilibrium thermodynamics as well as material scientists with a framework to consider in a systematic way several nonequilibrium questions about current developments, which are fostering new aims in heat transport, and the techniques for achieving them, for instance, defect engineering, dislocation engineering, stress engineering, phonon engineering, and nanoengineering. We also suggest some new applications in the particular case of mobile defects.

Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat Flux.

In this paper, we ask ourselves how non-local effects affect the description of thermodynamic systems with internal variables. Usually, one assumes that the internal variables are local, but that their evolution equations are non-local, i.e., for instance, that their evolution equations contain non-local differential terms (gradients, Laplacians) or integral terms with memory kernels. In contrast to this typical situation, which has led to substantial progress in several fields, we ask ourselves whether in some cases it would be convenient to start from non-local internal variables with non-local evolution equations. We examine this point by considering three main lengths: the observation scale R defining the elementary volumes used in the description of the system, the mean free path l of the microscopic elements of the fluid (particles, phonons, photons, and molecules), and the overall characteristic size L of the global system. We illustrate these ideas by considering three-dimensional rigid heat conductors within the regime of phonon hydrodynamics in the presence of thermal vortices. In particular, we obtain a generalization of the Guyer-Krumhansl equation, which may be of interest for heat transport in nanosystems or in systems with small-scale inhomogeneities.

Prostatic metaplasia and pilar differentiation in gender-affirming mastectomy specimens.

With the increasing practice of gender-affirming mastectomy as a therapeutic procedure in the setting of gender dysphoria, there has come a profusion of literature on the pathologic findings within these specimens. Findings reported in over 1500 patients have not included either prostatic metaplasia or pilar metaplasia of breast epithelium. We encountered both of these findings in the course of routine surgical pathology practice and therefore aimed to analyze these index cases together with a retrospective cohort to determine the prevalence, anatomic distribution, pathologic features, and associated clinical findings of prostatic metaplasia and pilar metaplasia in the setting of gender-affirming mastectomy. In addition to the 2 index cases, 20 additional archival gender-affirming mastectomy specimens were studied. Before mastectomies, all but 1 patient received testosterone cypionate, 6/22 patients received norethindrone, and 21/22 practiced breast binding. Prostatic metaplasia, characterized by glandular proliferation along the basal layer of epithelium in breast ducts, and in one case, within lobules, was seen in 18/22 specimens; 4/22 showed pilar metaplasia, consisting of hair shafts located within breast ducts, associated with squamoid metaplasia resembling hair matriceal differentiation. By immunohistochemistry, prostatic metaplasia was positive for PSA in 16/20 cases and positive for NKX3.1 in 15/20 cases. Forty-three reduction mammoplasty control cases showed no pilar metaplasia and no definite prostatic metaplasia, with no PSA and NKX3.1 staining observed. We demonstrate that prostatic metaplasia and pilar metaplasia are strikingly common findings in specimens from female-assigned-at-birth transgender patients undergoing gender-affirming mastectomy. Awareness of these novel entities in the breast is important, to distinguish them from other breast epithelial proliferations and to facilitate accrual of follow-up data for better understanding their natural history.

Relationships between rational extended thermodynamics and extended irreversible thermodynamics.

We consider a few conceptual questions on extended thermodynamics, with the aim to contribute to a higher contact between rational extended thermodynamics and extended irreversible thermodynamics. Both theories take a number of fluxes as independent variables, but they differ in the formalism being used to deal with the exploitation of the second principle (rational thermodynamics in the first one and classical irreversible thermodynamics in the second one). Rational extended thermodynamics is more restricted in the range of systems to be analysed, but it is able to obtain a wider number of restrictions and deeper specifications from the second law. By contrast, extended irreversible thermodynamics is more phenomenological, its mathematical formalism is more elementary, but it may deal with a wider diversity of systems although with less detail. Further comparison and dialogue between both branches of extended thermodynamics would be useful for a fuller deployment and deepening of extended thermodynamics. Besides these two approaches, one should also consider the Hamiltonian approach, formalisms with internal variables, and more microscopic approaches, based on kinetic theory or on non-equilibrium ensemble formalisms. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.

Bazedoxifene exhibits growth suppressive activity by targeting interleukin-6/glycoprotein 130/signal transducer and activator of transcription 3 signaling in hepatocellular carcinoma.

The interleukin (IL)-6/glycoprotein (GP)130/signal transducer and activator of transcription (STAT)3 pathway is emerging as a target for the treatment of hepatocellular carcinoma. IL-6 binds to IL-6R, forming a binary complex, which further combines with GP130 to transduce extracellular signaling by activating STAT3. Therefore, blocking the interaction between IL-6 and GP130 may inhibit the IL-6/GP130/STAT3 signaling pathway and its biological effects. It has been reported that bazedoxifene acetate (BAZ), a selective estrogen receptor modulator approved by the US Food and Drug Administration, could inhibit IL-6/GP130 protein-protein interactions. Western blot, immunofluorescence staining, wound healing and colony formation assays were used to detect the effect of BAZ on liver cancer cells. Cell viability was evaluated by MTT assay. Apoptosis of cells was determined using the Annexin V-FITC detection kit. Mouse xenograft tumor models were utilized to evaluate the effect of BAZ in vivo. Our data showed that BAZ inhibited STAT3 phosphorylation (P-STAT3) and expression of STAT3 downstream genes, inducing apoptosis in liver cancer cells. BAZ inhibited P-STAT3 induced by IL-6, but not by leukemia inhibitory factor. BAZ inhibited P-STAT1 and P-STAT6 less significantly as elicited by interferon-α, interferon-γ and IL-4. In addition, pretreatment of BAZ impeded the translocation of STAT3 to nuclei induced by IL-6. BAZ inhibited cell viability, wound healing and colony formation in vitro. Furthermore, tumor growth in HEPG2 mouse xenografts were significantly inhibited by daily intragastric gavage of BAZ. Our results suggest that BAZ inhibited the growth of hepatocellular carcinoma in vitro and in vivo, indicating another potential strategy for HCC prevention and therapy.

A novel small molecular STAT3 inhibitor, LY5, inhibits cell viability, cell migration, and angiogenesis in medulloblastoma cells.

Signal transducers and activators of transcription 3 (STAT3) signaling is persistently activated and could contribute to tumorigenesis of medulloblastoma. Numerous studies have demonstrated that inhibition of the persistent STAT3 signaling pathway results in decreased proliferation and increased apoptosis in human cancer cells, indicating that STAT3 is a viable molecular target for cancer therapy. In this study, we investigated a novel non-peptide, cell-permeable small molecule, named LY5, to target STAT3 in medulloblastoma cells. LY5 inhibited persistent STAT3 phosphorylation and induced apoptosis in human medulloblastoma cell lines expressing constitutive STAT3 phosphorylation. The inhibition of STAT3 signaling by LY5 was confirmed by down-regulating the expression of the downstream targets of STAT3, including cyclin D1, bcl-XL, survivin, and micro-RNA-21. LY5 also inhibited the induction of STAT3 phosphorylation by interleukin-6 (IL-6), insulin-like growth factor (IGF)-1, IGF-2, and leukemia inhibitory factor in medulloblastoma cells, but did not inhibit STAT1 and STAT5 phosphorylation stimulated by interferon-γ (IFN-γ) and EGF, respectively. In addition, LY5 blocked the STAT3 nuclear localization induced by IL-6, but did not block STAT1 and STAT5 nuclear translocation mediated by IFN-γ and EGF, respectively. A combination of LY5 with cisplatin or x-ray radiation also showed more potent effects than single treatment alone in the inhibition of cell viability in human medulloblastoma cells. Furthermore, LY5 demonstrated a potent inhibitory activity on cell migration and angiogenesis. Taken together, these findings indicate LY5 inhibits persistent and inducible STAT3 phosphorylation and suggest that LY5 is a promising therapeutic drug candidate for medulloblastoma by inhibiting persistent STAT3 signaling.

Tunable Heat-Flux Rectification in Graded Nanowires in Non-Linear Guyer-Krumhansl Regime.

We study heat rectification in composition-graded nanowires, with nonlocal and nonlinear effects taken into account in a generalized Guyer-Krumhansl equation. Using a thermal conductivity dependent on composition and temperature, the heat equation is solved. Introducing a non-vanishing heat supply (as for instance, a lateral radiative heat supply), we explore the conditions under which either nonlocal or nonlinear effects or both contribute to heat rectification and how they may be controlled by means of the external radiative flux. The corresponding rectification coefficients are calculated as well, and the physical conditions under which the system becomes a thermal diode are pointed out.

Impact of a Modified HistoGel Method for Processing Endocervical Curettage Specimens on Diagnostic Yield.

OBJECTIVES: Endocervical curettage (ECC) specimens may be limited by scant tissue. We evaluated whether a cellular concentration processing method could improve their diagnostic quality. METHODS: Between October 2018 and June 2019, ECC specimens were assigned chronologically to one of two groups: nonconcentrated ECC (NECC) or concentrated ECC (CECC). NECC specimens underwent routine histologic processing. CECC specimens were processed using a published HistoGel-based cell block method. We reviewed diagnoses for ECCs, concurrent cervical biopsies and/or loop electrosurgical excision procedures (LEEPs), and preceding Papanicolaou (Pap) smears. We performed multivariate logistic regression analyses to evaluate the impact of processing method on ECC adequacy and discordance between Pap smear and worst tissue diagnoses. RESULTS: NECC and CECC adequacy was 88.2% and 84.7% (P = .06). ECC adequacy was greater if concurrent biopsy/LEEP was performed (odds ratio [OR] = 1.76, P < .01). Discordance between Pap smear and worst tissue diagnoses was 9.5% and 13.3% (P = .04) for cases with NECC and CECC processing, although processing method was not significant in multivariate analysis (OR = 0.74, P = .11). Adequate ECC sampling and concurrent biopsy/LEEP were independently associated with concordance between Pap smear and worst tissue diagnosis (OR = 0.46, P < .01 and OR = 0.65, P = .02). CONCLUSIONS: ECC processing method did not significantly affect either specimen adequacy (P = .06) or diagnostic discordance (P = .11) when controlled for other factors.

The bioelements, the elementome, and the biogeochemical niche.

Every living creature on Earth is made of atoms of the various bioelements that are harnessed in the construction of molecules, tissues, organisms, and communities, as we know them. Organisms need these bioelements in specific quantities and proportions to survive and grow. Distinct species have different functions and life strategies, and have therefore developed distinct structures and adopted a certain combination of metabolic and physiological processes. Each species is thus also expected to have different requirements for each bioelement. We therefore propose that a "biogeochemical niche" can be associated with the classical ecological niche of each species. We show from field data examples that a biogeochemical niche is characterized by a particular elementome defined as the content of all (or at least most) bioelements. The differences in elementome among species are a function of taxonomy and phylogenetic distance, sympatry (the bioelemental compositions should differ more among coexisting than among non-coexisting species to avoid competitive pressure), and homeostasis with a continuum between high homeostasis/low plasticity and low homeostasis/high plasticity. This proposed biogeochemical niche hypothesis has the advantage relative to other associated theoretical niche hypotheses that it can be easily characterized by actual quantification of a measurable trait: the elementome of a given organism or a community, being potentially applicable across taxa and habitats. The changes in bioelemental availability can determine genotypic selection and therefore have a feedback on ecosystem function and organization, and, at the end, become another driving factor of the evolution of life and the environment.

The influence of non-modifiable and modifiable factors on cardiac biomarkers after marathon running.

BACKGROUND: This study investigated the influence of modifiable (training) and non-modifiable factors (age and gender) on cardiac troponin I (cTnI) and B-type natriuretic peptide (BNP) levels post-marathon. METHODS: Thirteen female and nine male recreational runners participated in the 2015 Hartford Marathon. A venous blood draw was taken from each subject at 24 hours pre-race, immediately post-race and 24 hours post-race. RESULTS: Weekly mileage and weekly long runs were recorded for a 12-week period prior to the marathon. No association was found between age and BNP (P=0.11, P=0.50) or cTnI (P=0.69, P=0.28) for either post-race time points. No association was found between gender and cTnI for either post-race time points (P=0.09, P=0.57). However, BNP elevation, at 24 hours post-race was more pronounced in females than males (P=0.047). For cTnI levels immediately post-race, a negative association was found for average weekly mileage (P=0.006), while a positive association was found for the number of long runs exceeding 20 miles (P=0.05). No association between training and BNP were found. CONCLUSIONS: These results suggest that female runners may experience greater cardiac stress than males. In addition, runners with greater weekly training mileage experienced less cardiac stress post-race, while runners who ran too many 20+ mile long runs, experienced more cardiac stress post-marathon.

Ursolic acid prevents angiotensin II-induced abdominal aortic aneurysm in apolipoprotein E-knockout mice.

BACKGROUND AND AIMS: Abdominal aortic aneurysms (AAA) is a chronic inflammatory disease in which signal transducer and activator of transcription 3 (STAT3), and disintegrin and metalloproteinase 17 (ADAM17) play important roles. However, it remains unclear whether ursolic acid (UA), a natural pentacyclic triterpenoid carboxylic acid, can have an impact on STAT3 and ADAM17 and hence influence the formation of AAA. The objective of this study was to characterize the potential effect of UA on the pathogenesis of AAA and on STAT3 and ADAM17. METHODS: Male ApoE-/- mice were infused with angiotensin II (AngII) (1000 ng/kg/min) for 4 weeks to induce AAAs. Daily intragastric gavage with 100 mg/kg UA or tap water containing Tween 80 as controls was provided. Immunohistochemistry, cell viability assay, colony formation, wound healing assay, and Western blot were used to explore the potential effect of UA on AAA. RESULTS: UA decreased the incidence of AngII-induced AAA in mice. UA alleviated the degradation of elastin fibers and inflammation and decreased the expression of MMP2, MMP9, ADAM17 and phospho-STAT3 (pSTAT3) in aorta of mice induced with AngII. UA inhibited the constitutive and stimuli-induced (AngII and tumor necrosis factor-α) expression of MMP2, MMP9, ADAM17 and pSTAT3 in vascular smooth muscle cells (VSMCs). Furthermore, UA decreased cell viability, and suppressed colony formation and wound healing in vitro. CONCLUSIONS: We demonstrated that UA ameliorated the severity of AAA and exhibited an inhibitory effect on the expression of pSTAT3 and ADAM17. UA might emerge as a promising agent contributing to the prevention or treatment of AAA.

Hamiltonian and Godunov structures of the Grad hierarchy.

The time evolution governed by the Boltzmann kinetic equation is compatible with mechanics and thermodynamics. The former compatibility is mathematically expressed in the Hamiltonian and Godunov structures, the latter in the structure of gradient dynamics guaranteeing the growth of entropy and consequently the approach to equilibrium. We carry all three structures to the Grad reformulation of the Boltzmann equation (to the Grad hierarchy). First, we recognize the structures in the infinite Grad hierarchy and then in several examples of finite hierarchies representing extended hydrodynamic equations. In the context of Grad's hierarchies, we also investigate relations between Hamiltonian and Godunov structures.

Growth-suppressive activity of raloxifene on liver cancer cells by targeting IL-6/GP130 signaling.

BACKGROUND: Interleukin-6 (IL-6) is a multifunctional cytokine, which is involved in the regulation of differentiation and growth of certain types of tumor cells. Constitutive activation of Signal Transducer and Activator of Transcription 3 (STAT3) induced by IL-6 is frequently detected in liver cancer and has emerged as a viable molecular target for liver cancer treatment. However, few inhibitors targeting up-streams of STAT3 are available for the therapy of liver cancer. We reported the discovery of EVISTA (Raloxifene HCl) as novel inhibitor of IL-6/GP130 protein-protein interactions (PPIs) using multiple ligand simultaneous docking (MLSD) and drug repositioning. The possible effect of Raloxifene in STAT3 signaling or liver cancer cells is still unclear. RESULTS: Raloxifene inhibited the P-STAT3 stimulated by IL-6, but not the induction of STAT1 and STAT6 phosphorylation by IFN-γ, IFN-α, and IL-4. Raloxifene inhibited STAT3 phosphorylation and resulted in the induction apoptosis on human liver cancer cell-lines. Raloxifene inhibited the targets of STAT3, such as Bcl-2, Bcl-xl and survivin and cell viability, cell migration, and colony formation in liver cancer cells. Further, daily administration of Raloxifene suppressed the Hep-G2 tumor growth in mice in vivo. MATERIALS AND METHODS: The inhibitory effect on STAT3 phosphorylation and activity as well as cell viability, migration, and colony forming ability by Raloxifene was examined in human liver cancer cells. Tumor growth was detected via mouse xenograft tumor mode. CONCLUSIONS: Our results suggest that Raloxifene is a potent IL-6/GP130 inhibitor and may be a chemoprevention agent for liver cancer by targeting persistent STAT3 signaling.

STAT3 as a potential therapeutic target in ALDH+ and CD44+/CD24+ stem cell-like pancreatic cancer cells.

Persistent activation of signal transducers and activators of transcription 3 (STAT3) is commonly detected in many types of cancer including pancreatic cancer. Whether STAT3 is activated in stem cell-like pancreatic cancer cells and the effect of STAT3 inhibition, is still unknown. Flow cytometry was used to isolate pancreatic cancer stem-like cells which are identified by both aldehyde dehydrogenase (ALDH)-positive (ALDH+) as well as cluster of differentiation (CD) 44-positive/CD24-positive subpopulations (CD44+/CD24+). STAT3 activation and the effects of STAT3 inhibition by STAT3 inhibitors, LLL12, FLLL32, and Stattic in ALDH+ and CD44+/CD24+ cells were examined. Our results showed that ALDH+ and CD44+/CD24+ pancreatic cancer stem-like cells expressed higher levels of phosphorylated STAT3, an active form of STAT3, compared to ALDH-negative (ALDH-) and CD44-negative/CD24-negative (CD44-/CD24-) pancreatic cancer cells, suggesting that STAT3 is activated in pancreatic cancer stem-like cells. Small molecular STAT3 inhibitors inhibited STAT3 phosphorylation, STAT3 downstream target gene expression, cell viability, and tumorsphere formation in ALDH+ and CD44+/CD24+ cells. Our results indicate that STAT3 is a novel therapeutic target in pancreatic cancer stem-like cells and inhibition of activated STAT3 in these cells by STAT3 inhibitors may offer an effective treatment for pancreatic cancer.

A novel small molecule STAT3 inhibitor, LY5, inhibits cell viability, colony formation, and migration of colon and liver cancer cells.

Signal Transducer and Activator of Transcription 3 (STAT3) is persistently activated in human liver and colon cancer cells and is required for cancer cell viability, survival and migration. Therefore, inhibition of STAT3 signaling may be a viable therapeutic approach for these two cancers. We recently designed a non-peptide small molecule STAT3 inhibitor, LY5, using in silico site-directed Fragment-based drug design (FBDD). The inhibitory effect on STAT3 phosphorylation, cell viability, migration and colony forming ability by LY5 were examined in human liver and colon cancer cells. We demonstrated that LY5 inhibited constitutive Interleukin-6 (IL-6)-induced STAT3 phosphorylation, STAT3 nuclear translocation, decreased STAT3 downstream targeted gene expression and induced apoptosis in liver and colon cancer cells. LY5 had little effect on STAT1 phosphorylation mediated by IFN-γ. Inhibition of persistent STAT3 phosphorylation by LY5 also inhibited colony formation, cell migration, and decreased the viability of liver cancer and colon cancer cells. Furthermore, LY5 inhibited STAT3 phosphorylation and suppressed colon tumor growth in a mouse model in vivo. Our results suggest that LY5 is a potent STAT3 inhibitor and may be a potential drug candidate for liver and colon cancer therapy.

Diffuse-interface model for rapid phase transformations in nonequilibrium systems.

A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describe transformations within the diffuse interface, we use the phase-field model which allows us to follow steep but smooth changes of phase within the width of the diffuse interface. Governing equations of the phase-field model are derived for the hyperbolic model, a model with memory, and a model of nonlinear evolution of transformation within the diffuse interface. The consistency of the model is proved by the verification of the validity of the condition of positive entropy production and by outcomes of the fluctuation-dissipation theorem. A comparison with existing sharp-interface and diffuse-interface versions of the model is given.

Measuring nonequilibrium temperature of forced oscillators.

The meaning of temperature in nonequilibrium thermodynamics is considered by using a forced harmonic oscillator in a heat bath, where we have two effective temperatures for the position and the momentum, respectively. We propose a concrete model of a thermometer to testify the validity of these different temperatures from the operational point of view. It is found that the measured temperature depends on a specific form of interaction between the system and a thermometer, which means that the zeroth law of thermodynamics cannot be immediately extended to nonequilibrium cases.

Drug design targeting protein-protein interactions (PPIs) using multiple ligand simultaneous docking (MLSD) and drug repositioning: discovery of raloxifene and bazedoxifene as novel inhibitors of IL-6/GP130 interface.

The IL-6/GP130/STAT3 pathway is critical for the progression of multiple types of cancers. We report here the discovery of raloxifene and bazedoxifene as novel inhibitors of IL-6/GP130 protein-protein interactions (PPIs) using multiple ligand simultaneous docking (MLSD) and drug repositioning approaches. Multiple drug scaffolds were simultaneously docked into hot spots of GP130 D1 domain by MLSD to compete with the key interacting residues of IL-6, followed by tethering to generate virtual hit compounds. Similarity searches of virtual hits on drug databases identified raloxifene and bazedoxifene as potential inhibitors of IL-6/GP130 interaction. In cancer cell assays both compounds bind to GP130 and demonstrated selective inhibition of IL-6 induced STAT3 phosphorylation and were significantly more potent than the previously reported natural product inhibitor MDL-A. The identified drugs represent a new class of lead compounds with piperidine, benzothiophene, and indole scaffolds to inhibit IL-6 induced homodimerization of GP130. Besides potential direct usage for clinic trials, the two compounds can also serve as lead compounds for optimization to speed the development of drugs selectively targeting the IL-6/GP130/STAT3 cancer signaling pathway.

Ursolic acid inhibits the growth of colon cancer-initiating cells by targeting STAT3.

BACKGROUND: We have previously reported Signal Transducer and Activator of Transcription 3 (STAT3) to be constitutively activated in aldehyde dehydrogenase (ALDH)(+)/cluster of differentiation-133 (CD133)(+) colon cancer-initiating cells. In the present study we tested the efficacy of inhibiting STAT3 signaling in human colon cancer-initiating cells by ursolic acid (UA), which exists widely in fruits and herbs. RESULTS: Our data demonstrated that UA inhibited STAT3 phosphorylation, and induced caspase-3 cleavage of ALDH(+)/CD133(+) colon cancer-initiating cells. UA also reduced cell viability and inhibited tumor sphere formation of colon cancer-initiating cells, more potently than two other natural compounds, resveratrol and capsaicin. UA also inhibited the activation of STAT3 induced by interleukin-6 in DLD-1 colon cancer cells. Furthermore, daily administration of UA suppressed HCT116 tumor growth in mice in vivo. CONCLUSION: Our results suggest STAT3 to be a target for colon cancer prevention. UA, a dietary agent, might offer an effective approach for colorectal carcinoma prevention by inhibiting persistently activated STAT3 in cancer stem cells.

Mesoscopic hydrothermodynamics of complex-structured materials.

Some experimental results in the study of disordered systems, polymeric fluids, solutions of micelles and surfactants, ionic-glass conductors, and others show a hydrodynamic behavior labeled "anomalous" with properties described by some kind of fractional power laws in place of the standard ones. This is a consequence of the fractal-like structure that is present in these systems of which we do not have a detailed description, thus impairing the application of the conventional ensemble formalism of statistical mechanics. In order to obtain a physical picture of the phenomenon for making predictions which may help with technological and industrial decisions, one may resort to different styles (so-called nonconventional) in statistical mechanics. In that way can be introduced a theory for handling such impaired situations, a nonconventional mesoscopic hydrothermodynamics (MHT). We illustrate the question presenting an application in a contracted description of such nonconventional MHT, consisting in the use of the Renyi approach to derive a set of coupled nonstandard evolution equations, one for the density, a nonconventional Maxwell-Cattaneo equation, which in a limiting case goes over a non-Fickian diffusion equation, and other for the velocity in fluids under forced flow. For illustration the theory is applied to the study of the hydrodynamic motion in several soft-matter systems under several conditions such as streaming flow appearing in electrophoretic techniques and flow generated by harmonic forces arising in optical traps. The equivalence with Lévy processes is discussed and comparison with experiment is done.