We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state systems. EPR-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product space. Remarkably, our loss function has an intimate connection with the steady entropy production rate (EPR), enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional (8D) limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

Errors are inevitable in information processing and transfer. While error correction is widely studied in engineering, the underlying physics is not fully understood. Due to the complexity and energy exchange involved, information transmission should be considered as a nonequilibrium process. In this study, we investigate the effects of nonequilibrium dynamics on error correction using a memoryless channel model. Our findings suggest that error correction improves as nonequilibrium increases, and the thermodynamic cost can be utilized to improve the correction quality. Our results inspire new approaches to error correction that incorporate nonequilibrium dynamics and thermodynamics, and highlight the importance of the nonequilibrium effects in error correction design, particularly in biological systems.

This paper presents theory and simulation of viscous dissipation in evolving interfaces and membranes under kinematic conditions, known as astigmatic flow, ubiquitous during growth processes in nature. The essential aim is to characterize and explain the underlying connections between curvedness and shape evolution and the rate of entropy production due to viscous bending and torsion rates. The membrane dissipation model used here is known as the Boussinesq-Scriven fluid model. Since the standard approaches in morphological evolution are based on the average, Gaussian and deviatoric curvatures, which comingle shape with curvedness, this paper introduces a novel decoupled approach whereby shape is independent of curvedness. In this curvedness-shape landscape, the entropy production surface under constant homogeneous normal velocity decays with growth but oscillates with shape changes. Saddles and spheres are minima while cylindrical patches are maxima. The astigmatic flow trajectories on the entropy production surface, show that only cylinders and spheres grow under the constant shape. Small deviations from cylindrical shapes evolve towards spheres or saddles depending on the initial condition, where dissipation rates decrease. Taken together the results and analysis provide novel and significant relations between shape evolution and viscous dissipation in deforming viscous membrane and surfaces.

Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. For the standard BTE, our results can recover the entropic frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT) as if there exists a well-defined effective thermal conductivity. For the fractional BTEs corresponding to the generalized Cattaneo equation (GCE) class, the entropy flux and entropy production rate will deviate from the forms in CIT and EIT. In these cases, the entropy flux and entropy production rate will contain fractional-order operators, which reflect memory effects.

Catalytic surface reaction networks exhibit nonlinear dissipative phenomena, such as bistability. Macroscopic rate law descriptions predict that the reaction system resides on one of the two steady-state branches of the bistable region for an indefinite period of time. However, the smaller the catalytic surface, the greater the influence of coverage fluctuations, given that their amplitude normally scales as the square root of the system size. Thus, one can observe fluctuation-induced transitions between the steady-states. In this work, a model for the bistable catalytic CO oxidation on small surfaces is studied. After a brief introduction of the average stochastic modelling framework and its corresponding deterministic limit, we discuss the non-equilibrium conditions necessary for bistability. The entropy production rate, an important thermodynamic quantity measuring dissipation in a system, is compared across the two approaches. We conclude that, in our catalytic model, the most favorable non-equilibrium steady state is not necessary the state with the maximum or minimum entropy production rate.

The analysis of cellular signaling cascades based on information thermodynamics has recently developed considerably. A signaling cascade may be considered a binary code system consisting of two types of signaling molecules that carry biological information, phosphorylated active, and non-phosphorylated inactive forms. This study aims to evaluate the signal transduction step in cascades from the viewpoint of changes in mixing entropy. An increase in active forms may induce biological signal transduction through a mixing entropy change, which induces a chemical potential current in the signaling cascade. We applied the fluctuation theorem to calculate the chemical potential current and found that the average entropy production current is independent of the step in the whole cascade. As a result, the entropy current carrying signal transduction is defined by the entropy current mobility.

Mesenchymal stromal cells (MSCs) were obtained from human bone marrow and amplified in cultures supplemented with human platelet lysate. Once semi-confluent, cells were seeded in solid collagen scaffolds that were rapidly colonized by the cells generating a 3D cell scaffold. Here, they acquired a myofibroblast phenotype and when exposed to appropriate chemical stimulus, developed tension and cell shortening, similar to those of striated and smooth muscle cells. Myofibroblasts contained a molecular motor-the non-muscle myosin type IIA (NMMIIA) whose crossbridge (CB) kinetics are dramatically slow compared with striated and smooth muscle myosins. Huxley\'s equations were used to determine the molecular mechanical properties of NMMIIA. Thank to the great number of NMMIIA molecules, we determined the statistical mechanics (SM) of MSCs, using the grand canonical ensemble which made it possible to calculate various thermodynamic entities such as the chemical affinity, statistical entropy, internal energy, thermodynamic flow, thermodynamic force, and entropy production rate. The linear relationship observed between the thermodynamic force and the thermodynamic flow allowed to establish that MSC-laden in collagen scaffolds were in a near-equilibrium stationary state (affinity ≪ RT), MSCs were also seeded in solid collagen scaffolds functionalized with the tripeptide Arg-Gly-Asp (RGD). This induced major changes in NMMIIA SM particularly by increasing the rate of entropy production. In conclusion, collagen scaffolds laden with MSCs can be viewed as a non-muscle contractile bioengineered tissue operating in a near-equilibrium linear regime, whose SM could be substantially modified by the RGD peptide.

Studies have reported that bio-cellular signal transduction can be investigated based on thermodynamics. This short article aims to consider signal transduction carried out by signaling molecules from the perspective of non-equilibrium thermodynamics. Under conditions in which total entropy production rate was minimized, the entropy production rate per signaling molecule was conserved independently of the steps during signal transduction. Accordingly, the conserved production rate can be defined as the channel capacity of the given signal transduction cascade. Non- equilibrium thermodynamics provides a theoretical framework for cell signal transduction.

A novel approach to flow injection analysis (FIA) was proposed based on the main principles of linear non-equilibrium thermodynamics (LNET). The basic principles of I. Prigogine theory for dissipative structures, internal entropy production rates, thermodynamic forces and fluxes arising in flow systems were shown to be applicable to FIA. The practical application of this novel FIA approach allowed the use of the extent of analytical reaction and the entropy production rates for flow system optimization, and in-depth understanding of the steady state. The FIA approach was also found to be a suitable technique for and characterizes its quality, explaining the peculiarities of short-term and long-term steady states in a FIA system and their role for reproducibility of practical measurements. The practical application o the FIA approach was found to support its theoretical principles and allow formulating an original manner to derive a basic equation in FIA theory.

The thermodynamical formalism of irreversible processes offers a theoretical framework appropriate to explain the complexity observed at the macroscopic level of dynamic systems. In this context, together with the theory of complex systems and systems biology, the thermodynamical formalism establishes an appropriate conceptual framework to address the study of biological systems, in particular cancer.The Chapter is organized as follows: In Subheading 1, an integrative view of these disciplines is offered, for the characterization of the emergence and evolution of cancer, seen as a self-organized dynamic system far from the thermodynamic equilibrium. Development of a thermodynamic framework, based on the entropy production rate, is presented in Subheading 2. Subheading 3 is dedicated to all tumor growth, as seen through a \"phase transitions\" far from equilibrium. Subheading 4 is devoted to complexity of cancer glycolysis. Finally, some concluding remarks are presented in Subheading 5.