The report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence: $$P\left(t\right)={P}_{0}exp{\left[\pm \left(t/\tau \right)\right]}^{\beta }$$P t = P 0 e x p ± t / τ β , and SM-2 is the Malthus-type relation with the time-dependent growth rate $$r(t)$$r ( t ) or relaxation time τ $$(t)=1/r(t)$$( t ) = 1 / r ( t ) : $$P\left(t\right)={P}_{0}exp\left(r\left(t\right)\times t\right)={P}_{0}exp\left[\tau \left(t\right)/t\right]$$P t = P 0 e x p r t × t = P 0 e x p τ t / t . Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~ 3 billion): from the compressed exponential behavior ( $$\beta >1)$$β > 1 ) to the stretched exponential one ( $$\beta <1$$β < 1 ). For SM-2 dependence, linear changes of $$\tau \left(T\right)$$τ T during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior $$P\left(t\right)={P}_{0}exp\left[b{\prime}t/\left({T}_{C}-t\right)\right]$$P t = P 0 e x p b ′ t / T C - t , where $${T}_{C}\approx 2216$$T C ≈ 2216 is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis.

The global population P(t) (growth from 10,000 BCE to 2023) is discussed in frames of the Verhulst-type scaling, recalling the sustainable development concept. The analysis focuses on the per capita global population growth rate, for which the analytic counterpart is considered: GP(P)=(dP(t)P(t))dt=dlnP(t)dt . The focused insight reveals two near- linear domains for GP(P) changes: from ~ 700 CE till ~1968 and from ~1968 till 2023. It can be considered a reference pattern for long-term global population changes. For models recalling the Verhulst-type scaling, such analysis indicates that a single pair of growth rate and system resource coefficients (r,s) should describe the rise in the global population. However, the Verhulst relation with such effective parameters does not describe P(t) changes, which raises the question of whether it is adequate to describe global population changes. Notably is the new way of data preparation, based on their collections from various sources and numerical filtering to obtain a ‘smooth’ optimal set. The changes of P(t) were analyzed via the ‘reversed protocol’ analysis, in comparison to the standard pattern, namely: (i) first, the linearized, distortions-sensitive transformation of P(t) data is carried out; it indicates domains where the validated application of a given scaling equation is possible and yields optimal values of relevant parameters, (ii) the final fitting via the selected scaling equation is carried out for identified domains, and using obtained optimal values of parameters. The analysis reveals links between GP(P) local ‘disturbations’ and some historical and prehistorical reference events, showing their global scale impacts.

The nonlinear dielectric effect describes changes of dielectric permittivity induced by the strong electric field. This report shows the evidence for the critical-like pretransitional behavior for the liquid-solid transition in the supercooled nitrobenzene. Hallmarks of such behavior extend even above the melting temperature. A method for the analysis of pretransitional effects, avoiding the biasing impact of the noncritical background contribution, is proposed.

The report examines food availability and demand in the Anthropocene era, exploring the connections between global population growth and carrying capacity through an extended version of Cohen’s Condorcet concept. It recalls the super-Malthus and Verhulst-type scalings, matched with the recently introduced analytic relative growth rate. It focuses particularly on the ongoing Fifth Industrial Revolution (IR) and its interaction with the concept of a sustainable civilization. In this context, the significance of innovative food preservation technologies that can yield high-quality foods with health-promoting features, while simultaneously increasing food quantities and reducing adverse environmental impacts, is discussed. To achieve this, high-pressure preservation and processing (HPP) can play a dominant role. High-pressure ‘cold pasteurization’, related to room-temperature processing, has already achieved a global scale. Its superior features are notable and are fairly correlated with social expectations of a sustainable society and the technological tasks of the Fifth Industrial Revolution. The discussion is based on the authors’ experiences in HPP-related research and applications. The next breakthrough could be HPP-related sterilization. The innovative HPP path, supported by the colossal barocaloric effect, is presented. The mass implementation of pressure-related sterilization could lead to milestone societal, pro-health, environmental, and economic benefits.

The report addresses quests related to innovative methods of food preservation in the context of the Industrial Revolutions epoch and the assisted population boost. Particular attention is paid to the High-Pressure Preservation/Processing (HPP) of foods that uniquely combine the pro-health expectations of 21st-century societies with the pro-environmental requirements of Sustainable Development. HPP technology also correlates with producers' and logistics' expectations due to the long period of fresh product quality preservation. Beneficial features of HPP technology and related physical foundations of high-pressure impact on foods are presented. HPP is related to “cold & high-pressure pasteurization” at near ambient temperature. This report also considers an innovative sterilization concept, linking colossal barocaloric effect (CBE) & HPP. It is related to compressing up to ~600MPa and high temperatures (90 C o − 120 C o ) controlled by the heat associated with CBE phenomenon. Further, the supplementary concept of ‘cold sterilization’ under medium-high pressures, supported by the reversed CBE, is presented.Finally, socioeconomic consequences of these unique technologies are discussed. They address 5th Industrial Revolution & Sustainable Development targets and expected new market niches.

The paper discusses global population changes from the beginning of the Anthropocene onset till 2024, based on the ‘tools’ and model concepts of Soft Matter dynamics. The ‘bottom-up’ approach, focused on the population data themselves and the distortion- sensitive validation of portrayal via a given scaling relation, is applied. Two exponential Super-Malthusian dependences are considered, namely (i) the empowered exponential one, and (ii) containing the time-dependent relaxation time. The latter follows the dominant linear pattern in the Industrial Revolution times, leading to ‘constrained and frustrated’ – type critical scaling for the global population growth. Finally, the evolution of the relative growth rate versus the population itself is considered. The link to the empowered exponential behavior is indicated. This contribution presents a new cognitive path for studying global population growth, exploring the Soft Matter dynamics approach. It offers a reliable fundamental base of derived scaling equations, including the meaning of relevant parameters. Studies revealed the non-monotonic nature of global population growth, where temporal local events can significantly influence leading trends. For Industrial Revolutions, the essential meaning of technological innovation in feedback alliance with socio-economic innovatively re-shaping surrounding is noted.