Organisms and ecosystems as ideal Carnot engines

Organisms and ecosystems as ideal Carnot engines

Introduction

Over the years, the concept of ecosystem has undergone a process of increasingly complex identification and subsequent scientific framework, thanks also to contributions from other disciplines; particularly those related to the energetic study of ecosystems, that is, all those processes that involve the transfer of energy in one or more ecological systems, and related to the relationships between living organisms and the physical environment (Odum E.P. and Barret G.W., 2006). It was above all the theory related to the dissipative structures of complex systems, and the irreversibility of their processes, that broadened the field of investigation and study (Prigogine I., Nicolis G., 1982). However, in its simplest and most immediate identification, each ecosystem can be defined as a unit consisting of one or more communities of living organisms (biotic elements) and non-living elements (abiotic elements) that interact with each other; a community is in turn a collection of multiple populations, each consisting of organisms of the same species. All populations interact with the abiotic component to form an ecosystem, in which a complex series of reciprocal interactions takes place in a dynamic and temporal equilibrium, also controlled by one or more physical-chemical feedback mechanisms, also called “feedback.” Feedback is a complex process whereby the results of a system’s actions are reflected in the system itself, correcting, adapting, and/or modifying its behavior and functioning.
From an energetic perspective, an ecosystem is an open thermodynamic system (a concept that will be explored further below), with characteristic and specific structures and functions determined by:
– energy flow;
– circulation of matter and energy (chemical, caloric, and mechanical) between the biotic and abiotic components.

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In particular, Ervin Bauer’s biological theory transcends the purely physical view of nature, proposing a “worldview” based on a universal principle from which the fundamental laws of life derive—metabolism, growth, reproduction, and reactivity—and distinguishing living organisms from machines through a three-level causality, with an autonomous and temporally active biological level. On this basis, the thermodynamic concept of exergy is applied to ecosystems as a holistic indicator of organization, development, and health, while its modified version, eco-exergy, measures a biological system’s distance from chemical equilibrium and the complexity of ecological processes. In short, life emerges not so much from the thermodynamic drive toward entropy, but from the kinetic dynamics of autocatalysis in biopolymeric systems, in which replication represents an extreme kinetic control, while thermodynamics only indirectly supports its processes.

However, to put it very simply, every living organism can be treated, as a first approximation and from a thermodynamic perspective, as an open system that interacts with its environment according to the first and second laws of thermodynamics. Specifically, under ideal reversibility assumptions, every organism can be assimilated to a heat engine operating between a “hot” source (solar or high-potential chemical energy) and a “cold” source (external environment). Consequently, the maximum work that can be extracted is limited by a Carnot efficiency.

Mathematical and Logical Proof

1. System Definition

Let’s consider an organism \(i\) as a control volume. This system:

receives energy from a high-quality source (solar radiation or chemical energy), characterized by an effective temperature \(T_{h,i}\),
releases heat to the external environment, at temperature \(T_c\),
converts part of the incoming energy into useful work \(W_i\) (biological work, growth, maintenance of electrochemical gradients).

2. Fundamental Balances

First Law:

$$
Q_{h,i} – Q_{c,i} = W_i \tag{1}
$$

Second Law (Clausius, integral form):

$$
\frac{Q_{h,i}}{T_{h,i}} – \frac{Q_{c,i}}{T_c} \le 0 \tag{2}
$$

3. Carnot Limit

From (2) we obtain:

$$
Q_{c,i} \ge Q_{h,i}\frac{T_c}{T_{h,i}}
$$

Substituting into (1):

$$
W_i \le Q_{h,i}\left(1 – \frac{T_c}{T_{h,i}}\right)
$$

The maximum efficiency is therefore:

$$
\eta_i^{\max} = \frac{W_i}{Q_{h,i}} \le 1 – \frac{T_c}{T_{h,i}} \tag{3}
$$

4. Extension to the chemical case

For chemical processes at constant temperature and pressure, the maximum non-expansion work is limited by the change in Gibbs free energy:

$$
W_i^{\max} \le -\Delta G
$$

5. Ecosystems with energy recycling

Considering the recycling of waste between organisms, the steady-state balance of the ecosystem can be formalized as:

$$
\boldsymbol{\dot{Q}}_{\mathrm{in}} = \boldsymbol{\dot{Q}}_\odot + \mathbf{\Phi}\big[(\mathbf{I}-\boldsymbol{\eta})\,\boldsymbol{\dot{Q}}_{\mathrm{in}} + \boldsymbol{\dot{R}}\big]
$$

The maximum extractable power is:

$$
\boldsymbol{\dot{W}}^{\max} = \boldsymbol{\eta}\,\boldsymbol{\dot{Q}}_{\mathrm{in}}
$$

Concluding summary

The proof shows that, assuming ideal reversibility conditions, every organism can be assimilated to a Carnot engine: the maximum extractable work is limited by the ratio between the temperatures of the hot and cold sources. In chemical processes, the equivalent limit is provided by the Gibbs free energy.

Applying the analogy to the entire ecosystem, the interaction between organisms through waste recycling can be represented as a network of interconnected Carnot engines. In this network, an increase in complexity (number of species, trophic interactions, and recycling cycles) leads to greater overall efficiency, reducing wasted energy.

Further exploration

Matrix analysis of energy flows to assess the effect of complexity on overall efficiency.
Nonlinear dynamic models that include internal irreversibilities and trophic feedback.
Calculation of ecological exergy to compare different ecosystems and demonstrate the effect of diversity on overall efficiency.

These approaches suggest that ecological complexity tends to increase overall thermodynamic efficiency, bringing it closer to the ideal limit defined by the second law of thermodynamics.

Guido Bissanti

Bibliography:

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Göran Wall G., Banhatti D.P. (2012). Exergy – a useful concept for ecology & sustainability. DOI:10.48550/arXiv.1111.3310

Jørgensen S.E., (1992). Exergy and ecology. https://doi.org/10.1016/0304-3800(92)90069-Q

Jørgensen S.E., Søren Nors Nielsen S. N. (2007). Application of exergy as thermodynamic indicator in ecology. https://doi.org/10.1016/j.energy.2006.06.011

Pross A. (2003). The driving force for life’s emergence: kinetic and thermodynamic considerations. https://doi.org/10.1006/jtbi.2003.3178

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