Research background: There is no doubt that innovation is an important source of economic growth. In the assessment of the innovative activity of Polish industrial processing enterprises, two opposing views can be found. The first indicates the exogenous shock resulting from the global financial crisis and the associated innovation crisis and the subsequent period of innovative pessimism. The second shows the Polish economy as the European Green Island due to strong and uninterrupted economic growth over the past 27 years, controlled inflation, and reduction of unemployment as well as increase of the citizens’ well-being. In these conditions, an interesting research gap appeared, which is worth filling, at the centre of which there are factors determining the innovative activity of enterprises, and in particular the role and importance of innovation barriers in various phases of the business cycle. Purpose of the article: The aim of the research is to determine the impact of innovation barriers and degrees of their importance on the innovation activity of Polish industrial processing enterprises during the business cycle. The time frame of the analysis covers three phases of the cycle: the prosperity period of 2004–2006, the global financial crisis of 2008–2010 and the recovery from 2012–2014. Methods: Pearson’s χ2 independence test and correspondence analysis were used for data analysis. The research results are presented in a graphical form of biplots that describe the coexistence of three types of variables: (1) types of enterprises and ownership sectors, (2) effects or objectives of innovative activity, and (3) innovation barriers and reasons for the lack of innovation. The basis of calculations were three databases covering the mentioned periods. Findings & Value added: High resistance of innovative activity of Polish industrial processing enterprises to economic fluctuations has been demonstrated. Innovation barriers and degrees of their importance had little impact on the operations of enterprises in the first of the analysed periods, when prosperity was booming. The impact of the global financial crisis on innovation activities proved to be counterintuitive, as enterprises have continuously achieved their goals and the importance of innovation barriers has diminished even more. In the third period, innovation barriers no longer had any significance for the innovation activities of enterprises. The phenomenon of a gradual decline in the importance of innovation barriers, regardless of the phases of the business cycle, was called the Polish Green Island Effect. The relationship found is a peculiarity which is probably unprecedented in recent world economic history.

Research background: The innovation activity of Polish industrial processing enterprises is examined in a broader time context than typical business cycle frames, which makes it possible to look at the investigated problems from the perspective of Kondratieff waves. Purpose of the article: The aim of the research is to describe the combined effect of mutual interactions between the ownership and size of Polish industrial processing enterprises on the goals of innovative activity and their degree of importance for the further development of the innovativeness of those firms. These relations are examined in various phases of the business cycle. Additionally, taking secular changes into account made it possible to lend credence to the claim that the global financial crisis is a typical phenomenon for the breakthrough period between two Kondratieff waves. Methods: A characteristic feature of the applied method is the focus on the combined effect of the enterprise type and ownership structure on firms’ innovation over three periods: prosperity 2004–2006, crisis 2008–2010 and recovery 2012–2014. As regards statistical techniques, the Pearson’s χ^2 independence test and correspondence analysis were applied. The results of the research are presented in a graphic form in three- and two-dimensional correspondence maps, which indicate the co-occurrence of (1) ownership sectors and enterprise types taken together, and (2) effects (goals) of the innovative activity of enterprises, together with the degree of their influence (importance) for further innovative activity. Mutual interactions between ownership sectors and enterprise types were visually analysed, indicating significant features of the triangles representing them. Findings & Value added: A significant combined effect of the ownership sectors and enterprise types on firms’ innovative activity was found. There was a certain type of dynamic equilibrium between those variables, which changes depending on the business cycle phase. In the global financial crisis of 2008–2010, a surprising phenomenon was found, consisting of the growth of innovative activity in most enterprises as compared to the period of prosperity in 2004–2006. The enterprises achieved the goals assumed, and the degree of their importance proved the significant influence on further innovative activity of those firms. Additionally, it was demonstrated that in the period of recovery (2012–2014) mutual interactions between ownership and size eliminated the relationship between those variables and the goals of innovative activity, and eco-innovations proved to be directly subordinated to traditional types of innovations, mainly product and process innovations. Changes occurring in the last of the examined periods are related to the near-zero inertia of the entire industrial processing section, which allows to interpret the global financial crisis as a typical phenomenon for a breakthrough marking the end of one Kondratieff wave and the beginning of the next. Moreover, 2015 is identified as the year of breakthrough, ending the Fifth and beginning the Sixth Kondratieff Wave, which was related to the transition from the information and telecommunications revolution to the biomedical-hydrogen revolution. The calculations presented in this paper are consistent with those forecasts.

The aim of this paper is to examine the role of thermodynamics, and in particular, entropy, for the development of economics within the last 150 years. The use of entropy has not only led to a significant increase in economic knowledge, but also to the emergence of such scientific disciplines as econophysics, complexity economics and quantum economics. Nowadays, an interesting phenomenon can be observed; namely, that rapid progress in economics is being made outside the mainstream. The first significant achievement was the emergence of entropy economics in the early 1970s, which introduced the second law of thermodynamics to considerations regarding production processes. In this way, not only was ecological economics born but also an entropy-based econometric approach developed. This paper shows that non-extensive cross-entropy econometrics is a valuable complement to traditional econometrics as it explains phenomena based on power-law probability distribution and enables econometric model estimation for non-ergodic ill-behaved (troublesome) inverse problems. Furthermore, the entropy economics has accelerated the emergence of modern econophysics and complexity economics. These new directions of research have led to many interesting discoveries that usually contradict the claims of conventional economics. Econophysics has questioned the efficient market hypothesis, while complexity economics has shown that markets and economies function best near the edge of chaos. Quantum economics has already appeared on the horizon, which recognizes money as a fundamental measurement device in the economy. The development of these sciences may indicate the need to reformulate all mainstream economics from its foundations.